Distance signless Laplacian cospectrality & verification of examples (or lack thereof)

1098 days ago by reinh196

#### Defining the signless distance Laplacian def SignDistLapla(G): n=G.order() M=zero_matrix(QQ,n,n) for i in range(n): for j in range(i+1,n): x=G.distance(i,j) M[i,j]=x M[j,i]=x M[i,i]=M[i,i]+x M[j,j]=M[j,j]+x return M 
       
# Definition of transmission sequence def trs(G): n=G.order() ones = ones_matrix(n,1) dg=G.distance_matrix() trg=vector(dg*ones) trgs=trg.list() trgs.sort() return trgs # Checks if a graph is transmission regular def IsTrsReg(G): unique_list_t=[] trans=list(trs(G)) for y in trans: if y not in unique_list_t: unique_list_t.append(y) if len(unique_list_t)==1: return True else: return False 
       
#### COSPECTRALITY ##### 
       
### Distance cospectral mates on 5 vertices L5=[] for G in graphs.cospectral_graphs(5, matrix_function=SignDistLapla, graphs=lambda g: g.is_connected()): L5.append([i.graph6_string() for i in G]) L5 
       
[['D|g', 'Dxw']]
[['D|g', 'Dxw']]
### Distance cospectral mates on 6 vertices L6=[] for G in graphs.cospectral_graphs(6, matrix_function=SignDistLapla, graphs=lambda g: g.is_connected()): L6.append([i.graph6_string() for i in G]) L6 
       
[['E~wW', 'EzZW'], ['E|g_', 'Exw_'], ['E~{W', 'EzZw']]
[['E~wW', 'EzZW'], ['E|g_', 'Exw_'], ['E~{W', 'EzZw']]
### Distance cospectral mates on 7 vertices L7=[] for G in graphs.cospectral_graphs(7, matrix_function=SignDistLapla, graphs=lambda g: g.is_connected()): L7.append([i.graph6_string() for i in G]) L7 
       
[['F~~|G', 'Fn|^w'],
 ['F|_L?', 'FxGN?'],
 ['F~LKG', 'F|LLG'],
 ['F~lKG', 'F|lLG'],
 ['F~nKG', 'F|nLG'],
 ['Flm{?', 'F|h{?'],
 ['F|m{?', 'F|j{?'],
 ['F|skG', 'F|UkG'],
 ['Fl}l?', 'FxJ^G'],
 ['F~DKG', 'FlKlG'],
 ['F`}KO', 'F`{MO'],
 ['Fn|\\G', 'Fnl\\g'],
 ['F|aD?', 'FtaD_'],
 ['F~~\\G', 'Fn|^W'],
 ['F~NKG', 'F|NLG'],
 ['F~|\\G', 'Fn|^G'],
 ['F|}l?', 'FxJ~G'],
 ['F|lNG', 'F|NNG'],
 ['F~c[g', 'Fz{KW']]
[['F~~|G', 'Fn|^w'],
 ['F|_L?', 'FxGN?'],
 ['F~LKG', 'F|LLG'],
 ['F~lKG', 'F|lLG'],
 ['F~nKG', 'F|nLG'],
 ['Flm{?', 'F|h{?'],
 ['F|m{?', 'F|j{?'],
 ['F|skG', 'F|UkG'],
 ['Fl}l?', 'FxJ^G'],
 ['F~DKG', 'FlKlG'],
 ['F`}KO', 'F`{MO'],
 ['Fn|\\G', 'Fnl\\g'],
 ['F|aD?', 'FtaD_'],
 ['F~~\\G', 'Fn|^W'],
 ['F~NKG', 'F|NLG'],
 ['F~|\\G', 'Fn|^G'],
 ['F|}l?', 'FxJ~G'],
 ['F|lNG', 'F|NNG'],
 ['F~c[g', 'Fz{KW']]
### Distance cospectral mates on 8 vertices L8=[] for G in graphs.cospectral_graphs(8, matrix_function=SignDistLapla, graphs=lambda g: g.is_connected()): L8.append([i.graph6_string() for i in G]) L8 
       
WARNING: Output truncated!  
full_output.txt



[['GzZ{rK', 'GzZ]rK'],
 ['GxKm@O', 'G`{MP_'],
 ['G~UkTG', 'Gr]kRo', 'GvW[{c'],
 ['GbL||W', 'GzZx[c'],
 ['G~SkTG', 'GrMkRo'],
 ['Gj\\~VO', 'Gr}k\\['],
 ['G~UkVo', 'GzZ]xG'],
 ['Gzx|Ro', 'Gz[W^{'],
 ['G~[kX?', 'Gn[lX?'],
 ['GtqLD?', 'GxKn@?'],
 ['GbL|t[', 'GrX^]c'],
 ['GzO[P[', 'GrOY\\c'],
 ['GvikV?', 'Gb{kRo'],
 ['GrUkRo', 'GvW[[c'],
 ['Gbw{V?', 'Gbi{V?', 'Glc}DO'],
 ['G|GL@?', 'GxGN@?'],
 ['GzZ~pK', 'Gvy[{{'],
 ['G~j|Ro', 'Gv|\\[s'],
 ['GjL~VO', 'Gr]k\\['],
 ['Gb}kRo', 'Gv[W{c'],
 ['Gv[Y{c', 'GvTW{s'],
 ['GbL||w', 'GzZz[c'],
 ['Gnt|Ro', 'GrvnXK'],
 ['GvakTO', 'GzIlR?'],
 ['Gz[m~K', 'Gvx|Rw'],
 ['GtmMDo', 'Gv?N{c'],
 ['GfIkvG', 'GfblR_', 'Gr`|R_'],
 ['Gjil\\?', 'GjilTO'],
 ['GfDltw', 'GrvmPK'],
 ['Gr`|Ro', 'GrX\\[c'],
 ['G~b|Vo', 'Gv~X[s'],
 ['Gft|Rw', 'G~Zx[c'],
 ['GfZ}|G', 'Gv|X[s'],
 ['Gf{mvw', 'G~}lZ_'],
 ['GnIkvG', 'Grsk\\K'],
 ['G~~|P?', 'G~~nP?'],
 ['GzS}TG', 'GvS}TG'],
 ['GrllT?', 'GvEkTg'],
 ['Gvv}Xk', 'Gz|~Pk'],
 ['Gfk{VO', 'G~c{TG'],
 ['GnalP?', 'GjqlP?'],
 ['G|slP?', 'GxsnP?'],
 ['Gnv|P?', 'GvvnP?'],
 ['GxqlP?', 'GxJNH?'],
 ['G|Un@?', 'GxFnP?'],
 ['G|]n@?', 'GxNnP?'],
 ['GjWkvC', 'GbA{~C'],
 ['GzllT?', 'GvekTg'],
 ['GjtmRO', 'Gva[[['],
 ['G~\\~VO', 'G~j|Vo'],
 ['GbLl|O', 'GbDn|O'],
 ['GrPnpG', 'GvT[[C'],
 ['Gz[m~[', 'Gvz|Rw'],
 ['GzpW[S', 'GzbW[S'],
 ['GrX[|c', 'GrX[\\k'],
 ['GrQY\\c', 'GrWY\\c'],
 ['GtUn@?', 'GxFmP?'],
 ['G~ukVo', 'GzZ}xG'],
 ['GbX{V?', 'GbJ{V?'],

...

 ['G~IlP?', 'GxNn@?'],
 ['GvukVo', 'GzZnpG'],
 ['GzZ]pK', 'GrY[{{'],
 ['Gzsk\\K', 'GvS{\\K'],
 ['Gnt|Rw', 'G~Zz[c'],
 ['GrPNxG', 'GvTW{C'],
 ['GrQ]\\c', 'GzWY\\c'],
 ['G~P{XK', 'G~P]XK'],
 ['G~ukTG', 'Gr}kRo', 'Gv[[{c'],
 ['GrUKpG', 'GrQkpG'],
 ['Gt]n@?', 'GxNmP?'],
 ['Gfu[p?', 'GfF]h?'],
 ['Gru[p?', 'GfFmh?'],
 ['Gr\\k\\K', 'Grsk^K'],
 ['GbjlR_', 'GzPW\\S'],
 ['G~R{XK', 'Gv\\W{s'],
 ['GrukRo', 'Gv[[[c'],
 ['GzgnR_', 'GvikV_'],
 ['G~|~^W', 'G~|nt{'],
 ['GrdKPG', 'GrLKPG'],
 ['Gvg{VO', 'Gzk{TG'],
 ['G~[k|[', 'GvxX|s'],
 ['GbLl|W', 'GrZx[c'],
 ['GrY~xK', 'GvTY{{'],
 ['Gz[k~[', 'Gvr|Rw'],
 ['Gz{ltG', 'GbT{V{', 'GvQ^|C'],
 ['GzSm~K', 'Gfx|Rw'],
 ['GnV|P?', 'GnVnP?'],
 ['GbWkvS', 'GfA{vC'],
 ['Gb\\~TG', 'Gr\\ltG'],
 ['GzdkT?', 'GjlkT?'],
 ['Gbx{V?', 'Gbj{V?'],
 ['GpN^H?', 'GxNMX?'],
 ['GvRY|C', 'GvQ]\\c'],
 ['G~v|P?', 'G~vnP?'],
 ['GjTm\\K', 'GjSn\\K'],
 ['G~b|Ro', 'Gz|mPk'],
 ['GvZmtG', 'GvXntG'],
 ['Gz[k|K', 'GvS|\\K'],
 ['GxylP?', 'GxJnH?'],
 ['GrPmxG', 'GrT[{C'],
 ['GvR]|C', 'GvQ]|c'],
 ['G~Xm|G', 'GvZm|G'],
 ['GzsltG', 'GvQZ|C'],
 ['Gnb|Ro', 'GztmPk'],
 ['Gnj|Ro', 'Gv\\\\[s'],
 ['Gj}kRo', 'Gvy[[S'],
 ['GhxLH?', 'Gxsm@?'],
 ['G~F~~O', 'Gvf~^W', 'G~~nPk'],
 ['G|ylDO', 'Gx{nPO'],
 ['Gz[m|K', 'Gvs|\\K'],
 ['Gft|Ro', 'GrvmXK'],
 ['GrYkpG', 'Gr]KpG'],
 ['G~}kVo', 'GzZ~xG'],
 ['Gzil\\?', 'GzilTO'],
 ['Gbil\\?', 'GbilTO'],
 ['GvgkR_', 'GfkkR_'],
 ['GjSltG', 'GbSltg'],
 ['GrlkPG', 'GrnKPG'],
 ['Gr\\~VO', 'GnyntG']]
WARNING: Output truncated!  
full_output.txt



[['GzZ{rK', 'GzZ]rK'],
 ['GxKm@O', 'G`{MP_'],
 ['G~UkTG', 'Gr]kRo', 'GvW[{c'],
 ['GbL||W', 'GzZx[c'],
 ['G~SkTG', 'GrMkRo'],
 ['Gj\\~VO', 'Gr}k\\['],
 ['G~UkVo', 'GzZ]xG'],
 ['Gzx|Ro', 'Gz[W^{'],
 ['G~[kX?', 'Gn[lX?'],
 ['GtqLD?', 'GxKn@?'],
 ['GbL|t[', 'GrX^]c'],
 ['GzO[P[', 'GrOY\\c'],
 ['GvikV?', 'Gb{kRo'],
 ['GrUkRo', 'GvW[[c'],
 ['Gbw{V?', 'Gbi{V?', 'Glc}DO'],
 ['G|GL@?', 'GxGN@?'],
 ['GzZ~pK', 'Gvy[{{'],
 ['G~j|Ro', 'Gv|\\[s'],
 ['GjL~VO', 'Gr]k\\['],
 ['Gb}kRo', 'Gv[W{c'],
 ['Gv[Y{c', 'GvTW{s'],
 ['GbL||w', 'GzZz[c'],
 ['Gnt|Ro', 'GrvnXK'],
 ['GvakTO', 'GzIlR?'],
 ['Gz[m~K', 'Gvx|Rw'],
 ['GtmMDo', 'Gv?N{c'],
 ['GfIkvG', 'GfblR_', 'Gr`|R_'],
 ['Gjil\\?', 'GjilTO'],
 ['GfDltw', 'GrvmPK'],
 ['Gr`|Ro', 'GrX\\[c'],
 ['G~b|Vo', 'Gv~X[s'],
 ['Gft|Rw', 'G~Zx[c'],
 ['GfZ}|G', 'Gv|X[s'],
 ['Gf{mvw', 'G~}lZ_'],
 ['GnIkvG', 'Grsk\\K'],
 ['G~~|P?', 'G~~nP?'],
 ['GzS}TG', 'GvS}TG'],
 ['GrllT?', 'GvEkTg'],
 ['Gvv}Xk', 'Gz|~Pk'],
 ['Gfk{VO', 'G~c{TG'],
 ['GnalP?', 'GjqlP?'],
 ['G|slP?', 'GxsnP?'],
 ['Gnv|P?', 'GvvnP?'],
 ['GxqlP?', 'GxJNH?'],
 ['G|Un@?', 'GxFnP?'],
 ['G|]n@?', 'GxNnP?'],
 ['GjWkvC', 'GbA{~C'],
 ['GzllT?', 'GvekTg'],
 ['GjtmRO', 'Gva[[['],
 ['G~\\~VO', 'G~j|Vo'],
 ['GbLl|O', 'GbDn|O'],
 ['GrPnpG', 'GvT[[C'],
 ['Gz[m~[', 'Gvz|Rw'],
 ['GzpW[S', 'GzbW[S'],
 ['GrX[|c', 'GrX[\\k'],
 ['GrQY\\c', 'GrWY\\c'],
 ['GtUn@?', 'GxFmP?'],
 ['G~ukVo', 'GzZ}xG'],
 ['GbX{V?', 'GbJ{V?'],

...

 ['G~IlP?', 'GxNn@?'],
 ['GvukVo', 'GzZnpG'],
 ['GzZ]pK', 'GrY[{{'],
 ['Gzsk\\K', 'GvS{\\K'],
 ['Gnt|Rw', 'G~Zz[c'],
 ['GrPNxG', 'GvTW{C'],
 ['GrQ]\\c', 'GzWY\\c'],
 ['G~P{XK', 'G~P]XK'],
 ['G~ukTG', 'Gr}kRo', 'Gv[[{c'],
 ['GrUKpG', 'GrQkpG'],
 ['Gt]n@?', 'GxNmP?'],
 ['Gfu[p?', 'GfF]h?'],
 ['Gru[p?', 'GfFmh?'],
 ['Gr\\k\\K', 'Grsk^K'],
 ['GbjlR_', 'GzPW\\S'],
 ['G~R{XK', 'Gv\\W{s'],
 ['GrukRo', 'Gv[[[c'],
 ['GzgnR_', 'GvikV_'],
 ['G~|~^W', 'G~|nt{'],
 ['GrdKPG', 'GrLKPG'],
 ['Gvg{VO', 'Gzk{TG'],
 ['G~[k|[', 'GvxX|s'],
 ['GbLl|W', 'GrZx[c'],
 ['GrY~xK', 'GvTY{{'],
 ['Gz[k~[', 'Gvr|Rw'],
 ['Gz{ltG', 'GbT{V{', 'GvQ^|C'],
 ['GzSm~K', 'Gfx|Rw'],
 ['GnV|P?', 'GnVnP?'],
 ['GbWkvS', 'GfA{vC'],
 ['Gb\\~TG', 'Gr\\ltG'],
 ['GzdkT?', 'GjlkT?'],
 ['Gbx{V?', 'Gbj{V?'],
 ['GpN^H?', 'GxNMX?'],
 ['GvRY|C', 'GvQ]\\c'],
 ['G~v|P?', 'G~vnP?'],
 ['GjTm\\K', 'GjSn\\K'],
 ['G~b|Ro', 'Gz|mPk'],
 ['GvZmtG', 'GvXntG'],
 ['Gz[k|K', 'GvS|\\K'],
 ['GxylP?', 'GxJnH?'],
 ['GrPmxG', 'GrT[{C'],
 ['GvR]|C', 'GvQ]|c'],
 ['G~Xm|G', 'GvZm|G'],
 ['GzsltG', 'GvQZ|C'],
 ['Gnb|Ro', 'GztmPk'],
 ['Gnj|Ro', 'Gv\\\\[s'],
 ['Gj}kRo', 'Gvy[[S'],
 ['GhxLH?', 'Gxsm@?'],
 ['G~F~~O', 'Gvf~^W', 'G~~nPk'],
 ['G|ylDO', 'Gx{nPO'],
 ['Gz[m|K', 'Gvs|\\K'],
 ['Gft|Ro', 'GrvmXK'],
 ['GrYkpG', 'Gr]KpG'],
 ['G~}kVo', 'GzZ~xG'],
 ['Gzil\\?', 'GzilTO'],
 ['Gbil\\?', 'GbilTO'],
 ['GvgkR_', 'GfkkR_'],
 ['GjSltG', 'GbSltg'],
 ['GrlkPG', 'GrnKPG'],
 ['Gr\\~VO', 'GnyntG']]
### Distance cospectral mates on 9 vertices L9=[] for G in graphs.cospectral_graphs(9, matrix_function=SignDistLapla, graphs=lambda g: g.is_connected()): L9.append([i.graph6_string() for i in G]) L9 
       
WARNING: Output truncated!  
full_output.txt



[['Hn]n[EQ', 'Hl}nKEY'],
 ['H`{NV?G', 'HtIktE?'],
 ['HnKmhEH', 'HnEyJEH'],
 ['Hlhw]fS', 'Hlhg]nS'],
 ['H~chKMi', 'HndIJ]B'],
 ['Hl|mzUh', 'HlYn{f]'],
 ['HzsW]}i', 'H~kiHNj'],
 ['HndLN^H', 'HhYl{f]'],
 ['HzK{[Fk', 'HzD{[Fk'],
 ['Hle^[E_', 'H|EN[Eg'],
 ['HtgZKE?', 'HpYIwEA'],
 ['H~{lYeB', 'H~sl]eB'],
 ['HldN\\EB', 'HjdWNmB'],
 ['H~{MLUj', 'H~[nwEl'],
 ['Hl{}LUL', 'HnhG^}s'],
 ['HnK}{Ek', 'H~cI\\Uj'],
 ['Hlc}J]H', 'HlJg]us'],
 ['HlTnIeB', 'HnUgNeB'],
 ['HlciGF~', 'HlCnxEJ'],
 ['HlfzhF\\', 'H~om\\er'],
 ['Hn{nkUH', 'H|Gh]mv'],
 ['Hl]kmEQ', 'Hj|ILeB'],
 ['HlDmne[', 'H|TNHUx'],
 ['Hn]H[U?', 'HzMH{U?', 'H|BioEq'],
 ['H~sizEH', 'H~cmzEH'],
 ['Hj||[U?', 'H~Dw{}?'],
 ['Hn{j[UH', 'H|gx^Es'],
 ['H~EKkmi', 'HjlGNvB'],
 ['Hhd~NE[', 'Hhc~nE['],
 ['HnDijeL', 'HnCijfL'],
 ['HlS}xeH', 'H~dmhEH'],
 ['H~T{iEr', 'H|J[^es'],
 ['Hl[l^Fb', 'Hj|LXUf'],
 ['HnCi^uH', 'HlHG^mt'],
 ['Hj\\WLFx', 'H|}jGEX'],
 ['H~Cl]Mi', 'H|\\iHuX', 'HnC}~EH'],
 ['H~ugZUV', 'H~gi~M['],
 ['HnszZeB', 'H|dIJvZ'],
 ['HnejLEJ', 'HlDnHfX'],
 ['HlDzkM\\', 'H|n]HMB'],
 ['H|m[KF_', 'HxKllF_', 'HhKGN~`'],
 ['H~[i{Ek', 'H~[iwEl'],
 ['Hj]l]eQ', 'Hl}hmEb'],
 ['HjCh\\]i', 'HnsiJeH'],
 ['H|[yLmN', 'H|[yLe^'],
 ['H||iJUL', 'HhSj^fr'],
 ['H|\\XKU?', 'HlVX[U?'],
 ['HnVi~ur', 'H~Fm\\nN', 'Hn[}Nvl'],
 ['HhShMUy', 'HllILMH'],
 ['HlMh{E?', 'HlMh\\E?'],
 ['H|sk^Fb', 'HnDinfL'],
 ['H|LI^MH', 'H|TnKUH'],
 ['H|~jhej', 'HlujjF~'],
 ['HxC]\\Ea', 'H`kJhvG'],
 ['H|\\gJUn', 'H~flhFB'],
 ['HnlnhUj', 'Hnwg]~t'],
 ['H|~IJ^X', 'HnkK~e^'],
 ['H|TyIER', 'HnkjHEJ'],
 ['Hh{L{Vg', 'Hxk|LMg'],

...

 ['Hj\\j|}i', 'Hj[j|}y'],
 ['HxemNE[', 'Hl|i[EX'],
 ['H|Swy]R', 'HlDm^eX'],
 ['HnCl{Fg', 'HlThwFJ'],
 ['H~VgI^Z', 'Hlzx{fS'],
 ['H|gW^Eo', 'H|GW^eo'],
 ['H~}{KEQ', 'H|CN~Ei'],
 ['HhM~{EW', 'HnTLGFz'],
 ['HlTmmfR', 'HlunkUJ'],
 ['Htm~CE_', 'Hti~CEc'],
 ['H~UmhMH', 'HnUmxMH'],
 ['H~Em\\EL', 'H~EmLUL'],
 ['HnS~MMV', 'HnDyLvN'],
 ['HnUjKUX', 'HlDmh]h'],
 ['HlUmiFB', 'HlSmieR'],
 ['Hlu}NMW', 'H|shIU~', 'HnGK~F}'],
 ['HhE~}eW', 'H~llHMH'],
 ['H|T{iEr', 'HlJ[^es'],
 ['H~u{NEF', 'H~kjJEn'],
 ['HhcjMuW', 'HlHg]es'],
 ['HxFwMNh', 'H|FWNMk'],
 ['H|Si~Vj', 'H|}jjmH', 'H|unjmH'],
 ['Hl]H\\U?', 'HlMh{U?'],
 ['HhCmnF^', 'HjvMHVF'],
 ['HlvmXUH', 'HnTyjEL'],
 ['Hxcx{E_', 'H`g~kEc'],
 ['HzKH[mi', 'HlDy{EX', 'HlDy[E\\'],
 ['H|DIhuX', 'H~lYHEB'],
 ['Hxc|{E_', 'H`i~kEc'],
 ['HlUk}Fb', 'HjvKhVF'],
 ['HpK}CEA', 'H`K~?FA'],
 ['HnDLJEJ', 'HlDmhEX', 'HlDmHFX'],
 ['HhCnOE_', 'HlkKGU?'],
 ['Htm]KEA', 'H`]N{EA'],
 ['H|S{iEr', 'HlJ[]es'],
 ['Hl\\n]eR', 'H~~KHmF'],
 ['H|^XKU?', 'HlV\\[U?'],
 ['HjSj{my', 'HjTj{mi'],
 ['HzCK]Mi', 'HzCG]Mj'],
 ['H~[kNvr', 'H~kiNf|'],
 ['HnSgIFV', 'HhGL]FV'],
 ['HlDgkfc', 'HhMNKUW'],
 ['H~knhUL', 'H~~HLmB'],
 ['HhC}NFz', 'HlTl{eR'],
 ['H|eKCeO', 'HtiKDV?'],
 ['H|[n}EB', 'Hl|n[UH'],
 ['HnKn]UH', 'HlJH^ms'],
 ['Hh[kLER', 'HldjGEX'],
 ['Hl\\NhEh', 'Hl|MjEH'],
 ['HjM~KNg', 'HzM]KNk', 'HnKG~]['],
 ['Hj[n[EQ', 'Hl}mKEW'],
 ['H~~X[U?', 'H|}hnU?'],
 ['H|lMXVX', 'HlF}LfL'],
 ['Hx{jkEU', 'Hx[MnUW'],
 ['H|Sk{EO', 'H|Sl[EO'],
 ['H|mK{U?', 'H|iLdm?'],
 ['H~|~\\fl', 'H~vznmj'],
 ['H|DYNUX', 'HnLiMeL'],
 ['Hn\\INMH', 'Hhk^}Eo'],
 ['H|{inVj', 'HnFynmj']]
WARNING: Output truncated!  
full_output.txt



[['Hn]n[EQ', 'Hl}nKEY'],
 ['H`{NV?G', 'HtIktE?'],
 ['HnKmhEH', 'HnEyJEH'],
 ['Hlhw]fS', 'Hlhg]nS'],
 ['H~chKMi', 'HndIJ]B'],
 ['Hl|mzUh', 'HlYn{f]'],
 ['HzsW]}i', 'H~kiHNj'],
 ['HndLN^H', 'HhYl{f]'],
 ['HzK{[Fk', 'HzD{[Fk'],
 ['Hle^[E_', 'H|EN[Eg'],
 ['HtgZKE?', 'HpYIwEA'],
 ['H~{lYeB', 'H~sl]eB'],
 ['HldN\\EB', 'HjdWNmB'],
 ['H~{MLUj', 'H~[nwEl'],
 ['Hl{}LUL', 'HnhG^}s'],
 ['HnK}{Ek', 'H~cI\\Uj'],
 ['Hlc}J]H', 'HlJg]us'],
 ['HlTnIeB', 'HnUgNeB'],
 ['HlciGF~', 'HlCnxEJ'],
 ['HlfzhF\\', 'H~om\\er'],
 ['Hn{nkUH', 'H|Gh]mv'],
 ['Hl]kmEQ', 'Hj|ILeB'],
 ['HlDmne[', 'H|TNHUx'],
 ['Hn]H[U?', 'HzMH{U?', 'H|BioEq'],
 ['H~sizEH', 'H~cmzEH'],
 ['Hj||[U?', 'H~Dw{}?'],
 ['Hn{j[UH', 'H|gx^Es'],
 ['H~EKkmi', 'HjlGNvB'],
 ['Hhd~NE[', 'Hhc~nE['],
 ['HnDijeL', 'HnCijfL'],
 ['HlS}xeH', 'H~dmhEH'],
 ['H~T{iEr', 'H|J[^es'],
 ['Hl[l^Fb', 'Hj|LXUf'],
 ['HnCi^uH', 'HlHG^mt'],
 ['Hj\\WLFx', 'H|}jGEX'],
 ['H~Cl]Mi', 'H|\\iHuX', 'HnC}~EH'],
 ['H~ugZUV', 'H~gi~M['],
 ['HnszZeB', 'H|dIJvZ'],
 ['HnejLEJ', 'HlDnHfX'],
 ['HlDzkM\\', 'H|n]HMB'],
 ['H|m[KF_', 'HxKllF_', 'HhKGN~`'],
 ['H~[i{Ek', 'H~[iwEl'],
 ['Hj]l]eQ', 'Hl}hmEb'],
 ['HjCh\\]i', 'HnsiJeH'],
 ['H|[yLmN', 'H|[yLe^'],
 ['H||iJUL', 'HhSj^fr'],
 ['H|\\XKU?', 'HlVX[U?'],
 ['HnVi~ur', 'H~Fm\\nN', 'Hn[}Nvl'],
 ['HhShMUy', 'HllILMH'],
 ['HlMh{E?', 'HlMh\\E?'],
 ['H|sk^Fb', 'HnDinfL'],
 ['H|LI^MH', 'H|TnKUH'],
 ['H|~jhej', 'HlujjF~'],
 ['HxC]\\Ea', 'H`kJhvG'],
 ['H|\\gJUn', 'H~flhFB'],
 ['HnlnhUj', 'Hnwg]~t'],
 ['H|~IJ^X', 'HnkK~e^'],
 ['H|TyIER', 'HnkjHEJ'],
 ['Hh{L{Vg', 'Hxk|LMg'],

...

 ['Hj\\j|}i', 'Hj[j|}y'],
 ['HxemNE[', 'Hl|i[EX'],
 ['H|Swy]R', 'HlDm^eX'],
 ['HnCl{Fg', 'HlThwFJ'],
 ['H~VgI^Z', 'Hlzx{fS'],
 ['H|gW^Eo', 'H|GW^eo'],
 ['H~}{KEQ', 'H|CN~Ei'],
 ['HhM~{EW', 'HnTLGFz'],
 ['HlTmmfR', 'HlunkUJ'],
 ['Htm~CE_', 'Hti~CEc'],
 ['H~UmhMH', 'HnUmxMH'],
 ['H~Em\\EL', 'H~EmLUL'],
 ['HnS~MMV', 'HnDyLvN'],
 ['HnUjKUX', 'HlDmh]h'],
 ['HlUmiFB', 'HlSmieR'],
 ['Hlu}NMW', 'H|shIU~', 'HnGK~F}'],
 ['HhE~}eW', 'H~llHMH'],
 ['H|T{iEr', 'HlJ[^es'],
 ['H~u{NEF', 'H~kjJEn'],
 ['HhcjMuW', 'HlHg]es'],
 ['HxFwMNh', 'H|FWNMk'],
 ['H|Si~Vj', 'H|}jjmH', 'H|unjmH'],
 ['Hl]H\\U?', 'HlMh{U?'],
 ['HhCmnF^', 'HjvMHVF'],
 ['HlvmXUH', 'HnTyjEL'],
 ['Hxcx{E_', 'H`g~kEc'],
 ['HzKH[mi', 'HlDy{EX', 'HlDy[E\\'],
 ['H|DIhuX', 'H~lYHEB'],
 ['Hxc|{E_', 'H`i~kEc'],
 ['HlUk}Fb', 'HjvKhVF'],
 ['HpK}CEA', 'H`K~?FA'],
 ['HnDLJEJ', 'HlDmhEX', 'HlDmHFX'],
 ['HhCnOE_', 'HlkKGU?'],
 ['Htm]KEA', 'H`]N{EA'],
 ['H|S{iEr', 'HlJ[]es'],
 ['Hl\\n]eR', 'H~~KHmF'],
 ['H|^XKU?', 'HlV\\[U?'],
 ['HjSj{my', 'HjTj{mi'],
 ['HzCK]Mi', 'HzCG]Mj'],
 ['H~[kNvr', 'H~kiNf|'],
 ['HnSgIFV', 'HhGL]FV'],
 ['HlDgkfc', 'HhMNKUW'],
 ['H~knhUL', 'H~~HLmB'],
 ['HhC}NFz', 'HlTl{eR'],
 ['H|eKCeO', 'HtiKDV?'],
 ['H|[n}EB', 'Hl|n[UH'],
 ['HnKn]UH', 'HlJH^ms'],
 ['Hh[kLER', 'HldjGEX'],
 ['Hl\\NhEh', 'Hl|MjEH'],
 ['HjM~KNg', 'HzM]KNk', 'HnKG~]['],
 ['Hj[n[EQ', 'Hl}mKEW'],
 ['H~~X[U?', 'H|}hnU?'],
 ['H|lMXVX', 'HlF}LfL'],
 ['Hx{jkEU', 'Hx[MnUW'],
 ['H|Sk{EO', 'H|Sl[EO'],
 ['H|mK{U?', 'H|iLdm?'],
 ['H~|~\\fl', 'H~vznmj'],
 ['H|DYNUX', 'HnLiMeL'],
 ['Hn\\INMH', 'Hhk^}Eo'],
 ['H|{inVj', 'HnFynmj']]
### To find cospectral graphs on 10 vertices, first sort the graphs in to groups of potentially cospectral graphs Num1 = 545 Num2 = 5279 Num_Vertices = 10 L = [] for i in range(Num2): L.append([i,[]]) for G in graphs(Num_Vertices): if G.is_connected(): a=SignDistLapla(G).charpoly()(Num1) b = mod(a.floor(), Num2) if G.graph6_string() not in L[b][1]: L[b][1].append(G.graph6_string()) c = mod(a.ceil(), Num2) if G.graph6_string() not in L[c][1]: L[c][1].append(G.graph6_string()) 
       
### Checking within each group for sets with similar characteristic polynomial evaluated at a prime N=[] for i in range(Num2): K=[] M=[] for j in range(len(L[i][1])): a=SignDistLapla(Graph(L[i][1][j])).charpoly()(167) K.append([L[i][1][j],a]) for i in range(len(K)): A=[K[i][0]] for j in range(i+1,len(K)): if K[i][1]-K[j][1]==0: A.append(K[j][0]) if len(A)>1: N.append(A) 
       
### Checking each of these sets for cospectrality. This is our set of cospectral graphs on 10 vertices L10=[] for i in range(len(N)): K=[] M=[] for j in range(len(N[i])): a=SignDistLapla(Graph(N[i][j])).charpoly() K.append([N[i][j],a]) for i in range(len(K)): A=[K[i][0]] for j in range(i+1,len(K)): if K[i][1]-K[j][1]==0: A.append(K[j][0]) if len(A)>1: L10.append(A) 
       
print L10 
       
WARNING: Output truncated!  
full_output.txt



[['IbQGjMM}g', 'IfEiMMkZO'], ['InPHx}ii_', 'IrthkNyGW'], ['I~hKjniiG',
'IrVMlmjgW'], ['IvhGzM]iW', 'IrHWnnMm_'], ['IfQkluGhO', 'IrpK{EFeG'],
['IzPkxmGkO', 'IvxXgFIgW'], ['IbtWHeW|O', 'IvgHHFiWw'], ['IvqL|eWgO',
'InBW[U?~w'], ['IbR{J]ZjW', 'IbR{JU^jW'], ['IbR{J]ZjW', 'InF\\kewyo'],
['IbR{JU^jW', 'InF\\kewyo'], ['If_JHFIYo', 'I`WG`vswg'], ['IrMJ|^W]g',
'Iv\\NtMdhg'], ['IjPIz^mWG', 'IvONwEYno'], ['IrcNLEI]?', 'I|OKxEky?'],
['IvcLJNGNO', 'IfJJLEjm?'], ['InSMXnIjO', 'IvSgh^fZ?'], ['IbOlxNhI?',
'IfEg}E?ww'], ['Ib@M\\UhN_', 'Ib@M\\UhNO'], ['IbHGlmJNw', 'Ij\\J{egHo'],
['IjRZJNL]g', 'IzxzINJWW'], ['Ir[\\i^w^W', 'Iv\\myNZgW'], ['Ir[\\i^w^W',
'I~likeJ~O'], ['IrVHmMxyW', 'IzvhIejko'], ['Iv\\myNZgW', 'I~likeJ~O'],
['IzThyN\\gW', 'I~hZLEJjo'], ['Izw^~V~hw', 'I~~[~~Xig'], ['IvdH[Eg|O',
'IvDL[Eg|O'], ['IbKmNvnJO', 'Ij}k]EJ}O'], ['IvfkkEI{o', 'IzYlxMcm?'],
['I|ynXEAi_', 'Ix{NxFiI?'], ['IvImgEiG?', 'IrgmoEmG?'], ['IzQgjF|nW',
'IbDG|}nno'], ['IrSKjuNm?', 'IfIWNeNm_'], ['IzGLjf}iG', 'IfENze}M?'],
['Ibo[jUYh?', 'InDHKugWW'], ['Ib?JHeWmW', 'IbsWpmEg?'], ['Ij{mX}]yO',
'IrC~}UZxg'], ['IbXGnNM~_', 'Id^YhNX|?'], ['I~Tg|]Ggo', 'IbwNlewiW'],
['IbsNlEwiO', 'IzS{|NGI?'], ['IblMjuGiO', 'IblNhuGiO'], ['IblMjuGiO',
'IzG]zNgI?'], ['IblNhuGiO', 'IzG]zNgI?'], ['IjYj|NYio', 'InvH]Uwjo'],
['IfXh^uIXg', 'IvlHLmN]?'], ['IfAWL]wwW', 'IfAWH]wxW'], ['IzrwhN{Xg',
'IvmlL^GzO'], ['Ifr]lmIwW', 'Ir~YZ]J[?'], ['IfC\\XNHnW', 'IzRKtmei_'],
['Ij|MlUi]_', 'IjlNlUi]_'], ['I~eK^EW}O', 'IrXyIF~gW'], ['IvW]l^YlW',
'I~tzkFJJW'], ['IzD[WFGYw', 'IzD\\WFGWw'], ['IzDim^WIW', 'IrDik^xIW'],
['Iz|ZI^|wW', 'Iz~ZIN|wW'], ['IbNHKuw]o', 'IfujKFLIW'], ['IjEyMEhiW',
'IjEyMEjIW'], ['I~AIwEAhG', 'IzAIwEAxG'], ['Irw[[U?{G', 'Irg\\[U?{G'],
['IvwivEuG?', 'IfXjvEfG?'], ['Id}llUcG?', 'Ir{GS~t?G'], ['IbhyjfMi?',
'Ibgyjf]i?'], ['IbQYjeMj?', 'IbQIjeMj_'], ['IviHnEMi?', 'IfiLnEMi?'],
['IreGjMMiO', 'IrRGx]XgO'], ['IrskjMYxo', 'Irsgj]Yxo'], ['IjOiHm]zO',
'IrgzIMNWW'], ['Ivlwl^i}?', 'I~J^WnyiO'], ['IvN^XeXgW', 'Iv\\KYNYww'],
['IvN^XeXgW', 'IbxW|}`mg'], ['Ibc]LVWmO', 'If?j|elWG'], ['IvWKhUhiO',
'IrD|lUGgO'], ['IjQYnVlgO', 'I~Yg~FWgO'], ['IbQyxfWhO', 'IjoL{NWhO'],
['I~@JHMKWw', 'Ij?mNe\\[?'], ['If@Jz}WwG', 'IjQKZfg~?'], ['IjsKjNHiW',
'Irq\\ZFhM?'], ['Ib`KlmM]o', 'IbYMNFyM_'], ['Iri|JF|M?', 'Ity[|^@Z?'],
['IjiKN}ZN?', 'IzZyiVHgW'], ['Ir]|^MHM_', 'IjQzJnhN_'], ['IzUKZEwM?',
'IfCgIMZnO'], ['IvA]ZmkM?', 'IvANZmkM?'], ['IrT{wEGwW', 'IjYKzMUg?'],
['IvNn}^MgW', 'Irn~g^|WW'], ['IvfyzmWkW', 'Iv|YY^XiW'], ['Iv\\KYNYww',
'IbxW|}`mg'], ['IrWyhULhW', 'IzciKeJnO'], ['Ix{~}F{G?', 'I~JXT~|?G'],
['IvohU^GG?', 'IvsISsu?G'], ['Ij@Kje[nG', 'Id[GhvTxG'], ['IbrWjNZzg',
'IftghF|~O'], ['IzKMHexy?', 'Ib]MzMFg?'], ['InpmX~mi_', 'Izfg^fJyW'],
['Inn}LuYiG', 'IbP{nv^mO'], ['IbeyXeIy_', 'IrUkhM\\gO'], ['IbLGj]y}?',
'IfGiKnxyO'], ['IbLgj]i~O', 'Ir[[JFymW'], ['Ivh[jMjiO', 'IbVXke{yo'],
['IjFYhNJkw', 'IjXGpmnyo'], ['IbSLhU]hW', 'IjYg~FWgO'], ['IbSLhU]hW',
'IlRGlNBNO'], ['IjvGjNIhw', 'IrXlLfMMg'], ['IfVGxMXlO', 'IbX]JEmwW'],
['IjYg~FWgO', 'IlRGlNBNO'], ['Iz[\\JMMhW', 'IzLik]NgW'], ['In?JXeh{_',
'IvRWHNWYG'], ['IfQgN~XwW', 'IfON|UY{g'], ['IfQgN~XwW', 'Ib|{zuGm?'],
['IfuMlMW]g', 'IrjYH]ngW'], ['IbsGnEY]O', 'IfSX\\VJGG'], ['IfON|UY{g',
'Ib|{zuGm?'], ['IjSKxNGiG', 'IjG\\HnGZ?'], ['I~KNLnWjO', 'I~KNLNWzO'],
['IbFHjejN_', 'IbFHJejNo'], ['IfQMZf{m_', 'IfSk~MuhG'], ['IrG}ZElM_',
'IzTJkMJWW'], ['IzHhh^gG?', 'IzGhh^iG?'], ['I~wKxm\\G?', 'IbNzoFOjg'],
['Ib{IN}Mi?', 'Ib{NYmMi?'], ['Iv[^M~WNw', 'Iz^XnMxyW'], ['IzFXwEGlW',
'IzF\\wEGhW'], ['IfMygEhiW', 'IjmgYEi{O'], ['I~fNWEUIg', 'Ir`ltv^?G'],
['I|qK\\Eai?', 'I`{mXVgI?'], ['I|Xgy]`G?', 'Ix[Y|UcG?'], ['Ir_w~u]h?',
'IzvGhm\\gO'], ['Ir{JhuYi?', 'Ir[NlEI]_'], ['IreMjeIi?', 'I`ulLNoi?'],
['InXjHvmy_', 'Ir}[NUijW'], ['IrOj\\mYi?', 'IzFgKeY[W'], ['IjPzhm]j?',
'IbIzKm}jG'], ['IbciLmImO', 'IbciHmImo'], ['IrLLHEYi?', 'IrDLXEYi?'],
['Ir@Ll]mm?', 'IfHHNUi]o'], ['IbK{LvKgw', 'IjEwjeMiW'], ['Ifdw\\VigO',
'IfDw\\vigO'], ['IrvglEGkO', 'Ir@GjMnwG'], ['Ivq|jmGko', 'Iv~^gEYGw'],
['IvsK|EXgw', 'IzQ^zMMg?'], ['IzOLhM~{o', 'InuMxNwWg'], ['IbXkhNWxo',
'Ij\\HKMyJo'], ['Iv[{JeMhW', 'IvW\\mN[HW'], ['I~z~j}Z|W', 'I~z}~Mzno'],
['Ir]|JMZhw', 'Irz\\rMxig'], ['IrbgjMJw?', 'IragjMjw?'], ['If]I|MWyG',
'IbF\\[Ug]w'], ['Ib?HhN~Wg', 'Ib?Hhn~WG'], ['InGN|EG{_', 'IzWzzMCg?'],
['Irh[lE]M?', 'IjmmHUHgo'], ['IjaiNFwmo', 'I|W]xN@^?'], ['Ib]MLUI]?',
'IvOKw]WJo'], ['IfAKzVLN?', 'IfxYLEJMO'], ['IvOg\\nhG?', 'IjC\\GEMxg'],
['InOZ{MWjO', 'IjRKxmcio'], ['IrFIk}GkW', 'Iz?j[VYMG'], ['Ifsgn]zgo',
'IfSwjMzlo'], ['IzBw\\~sXW', 'IjBw\\~s\\W'], ['I~yXtmFg?',
'Izy\\tmFg?'], ['IbXKlE|G?', 'IjsJkmcG?'], ['IrXLxE[G?', 'I|QkYm`G?'],
['I~c{zeKiG', 'I|vJhF`Xo'], ['IziJjEIi?', 'IziKxEI{?'], ['IzpwjNYxO',
'Ir}kMemio'], ['Inhgh]yio', 'Id{gx^Rx_'], ['Iv{KlUKhO', 'IbFiIM^hW'],
['I~UllMigW', 'IrrKn]ZhO'], ['IbwHzeWgO', 'IboLzeWgO'], ['IvSG\\uWiO',
'IfwG\\uG{O'], ['I~U^XEI{o', 'InFiGE~xw'], ['IrTWJEjwW', 'Ib@MLfmMo'],
['IjY\\jEYlw', 'IbW[pnlzW'], ['IfBWzFNWw', 'IrTgLNNwW'], ['IfcMhFIYO',
'IrAG}FTeG'], ['I~?NjNnXw', 'If[x~u?}w'], ['IjZwjM~ZG', 'Ijt~Z~gY?'],
['IbxHLE]N_', 'IbpHLE]n_'], ['Ir|n|Uymg', 'If{[v}t~O'], ['IrZhJE~mg',
'IzW^rNdxO'], ['Iv]\\jMZnw', 'IvY{rm|~G'], ['Ir~lIMGiW', 'IbDHNNl]W'],
['IrFW{mXxW', 'IrFwNu][O'], ['IrUgINlGW', 'IrUGJNlGW'], ['Ivci|UHKO',
'Irkm|EHKO'], ['InSgIEIio', 'IbOGrMfx?'], ['IrOISdn?G', 'Ira[[CCeG'],
['IzUGneLm?', 'IbD\\KMxNo'], ['IrWIzeKiG', 'IrGIzeKig'], ['IbXgxEii_',
'Iz]GSduAG'], ['IjZIlEIiO', 'IvXKjEIiG'], ['Iffxj^Zi?', 'I~DLMFn\\o'],
['Iv[wneGxO', 'Ir[wnuGxO'], ['IjsN|EwiO', 'Iz\\LxNLI?'], ['IjsN|EwiO',
'IvpW{EVuG'], ['Ij{LhmyhO', 'Iryg~NWgo'], ['IbQGHuWgO', 'IrQWPUIGG'],
['InZ[jFYhW', 'Izw\\yNYHW'], ['InZ[jFYhW', 'Id}IhNX|W'], ['IvS\\jf}hW',
'IvJKNUZ~o'], ['Ir@ihN~wG', 'Iv{mZ]GM?'], ['IbgIzEY[?', 'IbWLhNhI?'],
['Ij|mZ]I[?', 'IzBN~FM[?'], ['Iz\\LxNLI?', 'IvpW{EVuG'], ['IjJWZmZ^w',
'I~kmkVHmw'], ['InB]nF]nW', 'I~nyNUHlo'], ['IvB{nmG~_', 'I~B{NmG~_'],
['Ib[xIN]G?', 'IpSLvE^G?'], ['IbRjLN{ho', 'Iz?y[^nWW'], ['InNZWmymO',
'InVi{vhWW'], ['I~U[GEwIw', 'Ir[kh~?go'], ['Izw\\yNYHW', 'Id}IhNX|W'],
['IvfmgEgiw', 'Ir{{p^Mg?'], ['IvfLwFMXW', 'IvdLwF]XW'], ['I~DGwmZgW',
'I~DGwNZgW'], ['I~}~imz^w', 'I~Vnl}n~o'], ['Ivw]wUHlw', 'Ifugt}dlG'],
['Ijc{]e?jG', 'InHW[^bGG'], ['Ivu[uESG?', 'Ivs[ueSG?'], ['IrOMtMeh?',
'IrOMvMch?'], ['If{[rM|zO', 'Ifw[r]|zO'], ['If}]WEwG?', 'I~RYWFUG?'],
['IjOKje]mG', 'IjSKje]iG'], ['InOG~eKi?', 'IjbKLUiM?'], ['Ijfy~fJiW',
'Iv[^m^wJW'], ['IzL~\\uyiG', 'Ibx{N}^kW'], ['IjcmL}]yO', 'InLXzMMiW'],
['IjRWHN\\iW', 'IjOW~]nGG'], ['IjYGxFYgO', 'If_i|eGWg'], ['IzQJxFYxO',
'IjQJxFY|O'], ['InR]hN{ko', 'IvtKyM]kw'], ['IbSMHMZiW', 'IjDXKNkMO'],
['Inx[HMYgO', 'Ib@MLmk}_'], ['In}WLu]}O', 'IvGIL}~jw'], ['Iz?nhNXWg',
'InIj|EG{_'], ['Ib@HhmZWG', 'IzZWpFAGG'], ['IjBxneH\\W', 'Ibpm\\^HYo'],
['IjBxneH\\W', 'Ir`][]Mdw'], ['Ibpm\\^HYo', 'Ir`][]Mdw'], ['Ij@nLemNO',
'IfdX~egHo'], ['IrbM\\eiM?', 'IrhyHUhgW'], ['IbQGJM}G?', 'IfCgVNHG?'],
['IfgJkmGwO', 'IrOxp]Mg?'], ['I~QxGNhxw', 'I~cm\\uhIW'], ['InHZNEJZo',
'IzCzLmJjO'], ['IjmjHUhgO', 'IjMjLUhgO'], ['IzFykM^xo', 'IzTz^VXXG'],
['InT|]Eo~G', 'InT|}EonG'], ['Id{yuU}G?', 'Itq}mUuG?'], ['Id{mvE}G?',
'IvmmsdV?G'], ['I~aK~EIg?', 'IzWhH^wGO'], ['IfKNXugiG', 'IfCNxugiG'],
['IfpiHumy_', 'IbYwzMywO'], ['IbXiHmniG', 'IlTghNd^?'], ['IbCmxmI}o',
'IbPWxmc~g'], ['IbDihmm}G', 'IvwWzeNgO'], ['Iv_mhmYi?', 'Iv?mxmYi?'],
['InUyHmI~O', 'IrgZ\\]JyW'], ['If`GneIj?', 'Ib`GjeInO'], ['IbfnXUIgO',
'IbBiNNhMO'], ['Ijd{JVGio', 'IfC{HVjko'], ['Iv\\Jx]GhO', 'In[z^EFGG'],
['IjyKhMiiO', 'IfDiKuLJW'], ['InUGlUMho', 'IjQX^MXM_'], ['InUGlUMho',
'IjRXNEZM_'], ['IfpGl][ko', 'IfpGh][mo'], ['Ij^wxFYwO', 'Inq[hMw{g'],
['IjPLLN{{w', 'Ir]]~E]M?'], ['Ij[{JFYwW', 'IbukMumgo'], ['If{wzUMgO',
'IbBW|^MNG'], ['Ir@gjmkWG', 'Ir@GjmlWG'], ['IfNWjMG]G', 'IzfgKEIiw'],
['IzPIZFkW?', 'IpSGV~HgO'], ['IjhhLEm]?', 'Ib[I[}wiO'], ['IjhhLEm]?',
'IjChKfngW'], ['IrBJNEnN_', 'IfMwNEMmW'], ['IjQX^MXM_', 'IjRXNEZM_'],
['IrQHLNYG?', 'IjQhoEKHg'], ['IjGxjMMG?', 'IbHxjMiG?'], ['IjPJKNxhO',
'IbEyIE^xO'], ['IfM}Gmyi?', 'IrFkKE]\\W'], ['Ir^IKmwyo', 'IzDgy^[iW'],
['Ir^IKmwyo', 'Indi{eJZO'], ['Ib[I[}wiO', 'IjChKfngW'], ['Irl{wEGIw',
'Ir\\gwFGYw'], ['Ir\\il}WiW', 'IjtN]MwjO'], ['IzDgy^[iW', 'Indi{eJZO'],
['IrnZINxWW', 'IrtNNNwIo'], ['Iv{]i}jhW', 'If[ymNmxw'], ['IbG[WFG]O',
'IjCh]EIGG'], ['I~|X}Ehiw', 'Ijriv}lig'], ['IzFwKeJWW', 'IrUiYUigo'],
['IbeiiEZjW', 'IbzKpmcio'], ['IrUh^VJGG', 'IrUj^FJGG'], ['I|{GHEgG?',
'Ix{GHFgG?'], ['Ifuk|UGi?', 'IzOnhEyI_'], ['IjiLjEgg?', 'IjJXPMeGG'],
['IvoNnEIg?', 'IfoN~EIg?'], ['IjCgzm~n_', 'IbY{hm{mw'], ['IrcNjuKiG',
'Ib[JHNYjo'], ['I~_I\\egi?', 'IzYGHnwGO'], ['IzflxE]zg', 'IjrnXNjyo'],
['IzPH|MIi?', 'IjpH|MIi?'], ['IrPGhuMm_', 'IbQGtncm_'], ['IzmIxEJkW',
'IzEmzVKM?'], ['IzmIxEJkW', 'IfU\\NUH]_'], ['IzmIxEJkW', 'IjHIKnxnO'],
['IzOIxUKxO', 'IrLIgNgYW'], ['IfWGlM{gW', 'IfWGl]kgW'], ['IfWGlM{gW',
'IbSMhMYwW'], ['IfWGl]kgW', 'IbSMhMYwW'], ['I~jgne{wO', 'IfBW|^^NG'],
['IfOGN~XgO', 'IvRwGM[hO'], ['IfW{jM}ho', 'Iv@jl^ym?'], ['I~IkxEkYG',
'InuLtMFg?'], ['IvIl|}G{o', 'Ib\\z}V^GG'], ['InpnLE]n?', 'IzQkJ}XnG'],
['IzEmzVKM?', 'IfU\\NUH]_'], ['IzEmzVKM?', 'IjHIKnxnO'], ['IvIKjFHM?',
'IdsGxVBXO'], ['IfU\\NUH]_', 'IjHIKnxnO'], ['IrE[NEwm?', 'IvKjMFgWO'],
['IjQh[MgG?', 'IrPh[MgG?'], ['IvAK[]GG?', 'Iv?N[cE?G'], ['IzOiGF\\GO',
'IzOiGE|GO'], ['IrlwgEGgw', 'Ib\\lgV?go'], ['IrVL{MiMw', 'IvVLvMehG'],
['IzZyg]HgW', 'IfXW\\e`mw'], ['InekiEMjO', 'IfPKpmcno'], ['I~mkmeIiW',
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['IfEiXMGxO', 'IfCiXMGzO'], ['IbQkhUGgO', 'Ir`G{cDEG'], ['IzO|xuGhO',
'Iv{ZWEK[W'], ['IfWWlE]hO', 'IjDhME{iO'], ['IzrGhMyho', 'IjcYhuMww'],
['IbU\\J}ihW', 'I~Kmg~GwW'], ['IbU\\J}ihW', 'IbRkpnkn_'], ['In{WLe~{W',
'Irf}HNW~g'], ['IjI{xMG{?', 'IrtIUKVCW'], ['Ib@jjMw[g', 'IzygIf\\GO'],
['IzjmLUL~?', 'Ij~hKMIzw'], ['IfBGlvNNO', 'Iz`y\\VJWG'], ['IbiXJ^XM_',
'IbiXJNxM_'], ['IvVHm]wyW', 'IfUMx]l~?'], ['IvxZYmXWW', 'IrmzJMXwW'],
['IrT|Me|Iw', 'In[ymNigw'], ['I~\\jMVgWO', 'I~LjNVgWO'], ['I~Kmg~GwW',
'IbRkpnkn_'], ['IrnnYUJiO', 'IbEyyEZ~o'], ['IzUnNemgo', 'Izrwpncz_'],
['I|Xgz]`G?', 'Ix[Z|UcG?'], ['IzPwjE\\mO', 'IbIwNezm_'], ['Ivel~UMi?',
'Ir}J\\UHiw'], ['IbNnLeImG', 'I~DikMWJw'], ['IfDG|EJjO', 'IrBiLEJMg'],
['I~JhzfizG', 'I~\\In}NgW'], ['I~JhzfizG', 'I~nmkUjmO'], ['Iv^klUGgO',
'IfPWNuLXW'], ['IbhhjEKwO', 'Ib`gL~I[?'], ['Ifo{zEMgO', 'IrI\\ZfGIo'],
['Ifpn\\eGWg', 'IbP[Lm]NO'], ['Ibe~JFlM?', 'IbHMgnl~?'], ['Ibe~JFlM?',
'InSz]EojG'], ['IbHMgnl~?', 'InSz]EojG'], ['I~\\In}NgW', 'I~nmkUjmO'],
['IvTim}gwW', 'Irtim}gwW'], ['IrgYY]JYw', 'IrgY]]JYW'], ['Ir]]gUHhW',
'IvSgzMigo'], ['IfLY\\EjMO', 'InuGzMchG'], ['IfKz[Fxiw', 'I|PI|Fj~?'],
['IjRw[]t\\W', 'IbuKv}dlO'], ['IpuKpUGg?', 'ItYM[EAG_'], ['IzZ|xECx?',
'I~{HpVmG_'], ['IvLwtV~?G', 'IzZLTf~?G'], ['I~{IVcCAG', 'Iz{JVcCAG'],
['IjGMjfK}G', 'IrQM~eMM?'], ['IbGIje[jw', 'IfDHX]G|g'], ['IbQGjMN~?',
'IjEmYEi{O'], ['IbONheYm?', 'Ivg\\[U?XG'], ['IfoN|fYi?', 'IzOY^VnGG'],
['IruNJeIi?', 'Ir}GxmWgO'], ['Ij?ijm]yG', 'IfhJj^Ii?'], ['InhhlNi}?',
'IbxmrNd|?'], ['IbqXlvWnO', 'IznXKngHo'], ['IfcXxvXlO', 'IbPKLmM~w'],
['If{MhEhiO', 'I~CH]V\\GG'], ['Ifjgjm[xO', 'Ivd|KMwio'], ['Ifjgjm[xO',
'I~dh^UgHo'], ['IzW~h^ZgW', 'IrDZMF~}o'], ['I~tWHeIgO', 'Iz|WHeIgO'],
['I~?m|f|XW', 'Izdjw}G|w'], ['IrWH\\EY}?', 'IrOH\\EY}_'], ['Ib`m\\^HYo',
'Ir`Y[]Mdw'], ['IrEKk]GG?', 'IvQ[OE?MG'], ['Ir[JKNYxW', 'IrUiImngo'],
['Ir\\i~M^iW', 'Ijvl]ej{o'], ['Irnm}m^{W', 'IfT~]Vnno'], ['IjTHKewYo',
'IbTHKuwYo'], ['Ivd|KMwio', 'I~dh^UgHo'], ['If\\LkNwIo', 'IbOnp]llG'],
['IjC~{UIwO', 'IvWjtMchG'], ['IjE\\?EWlG', 'IvNGOEWgg'], ['IjfHOEkIg',
'I~@hS{k?G'], ['I~YxnNIG?', 'I~YwnNiG?'], ['IrxgzN]xO', 'IrpgzM}xW'],
['I~`yLmYmG', 'IjakZUzMw'], ['I~`yLmYmG', 'Ijeg]VJ{w'], ['I~FinMZlW',
'IzFinNZlW'], ['IboHxUhio', 'IrDNgEWMw'], ['IfO\\hU[lO', 'IbPGpmejw'],
['If{WxMzhO', 'IzqNINyJO'], ['Ib@IhEhlO', 'IjOY\\eKGG'], ['IfFLXFwZO',
'Iro]rMdl?'], ['IfgHhEIWo', 'IjCKx^GI?'], ['IfGWXUw]G', 'Ifi|HFGHO'],
['IrHlZEiW?', 'IrWhZEmW?'], ['IbqGJmH~O', 'IzGKxN}I?'], ['InUX^eHM_',
'InQX^uHM_'], ['InA[JMXMO', 'InAKJMXmO'], ['IjakZUzMw', 'Ijeg]VJ{w'],
['IzZwGFWHW', 'I~|ITkCAG'], ['IrV\\i]H|W', 'Irg^g]z{W'], ['IvYyh]LhW',
'I|SljFfZO'], ['IfCmLugWW', 'IbUmIUZgO'], ['InfXoEagg', 'I|XMI]tG?'],
['IzSYmEMG?', 'IvDHvKd?G'], ['IryWjELm?', 'Ir_y\\UNWG'], ['IrQGn^Ln?',
'IfXhzmci_'], ['IjVIzvMy_', 'IbeXjF~Ng'], ['Iv{NHvhy_', 'IjDhj]~[g'],
['Iv{NHvhy_', 'If}NNnxg?'], ['Iz\\HHEYi?', 'IzlHHEYi?'], ['IzlKHEm}?',
'IvFIWEk|W'], ['IjuyXFJhw', 'IvQWZv]xO'], ['IvcixeGhO', 'IjWLL^KI_'],
['Ij_XxVGjO', 'IbPKNmMMG'], ['IfYK|MIho', 'IzelIUigo'], ['Iz\\|JF~gW',
'IzZ~NFj]?'], ['InAHxF[Yg', 'I~DWWEYhw'], ['In?wJVHZW', 'IziG]nFAG'],
['IrAghNKXG', 'IrOIWEW|o'], ['IfIGlMGZG', 'IjDgMEMIW'], ['IzYIlN]YG',
'IjcyG~H|o'], ['IjDhj]~[g', 'If}NNnxg?'], ['IjBiNei]O', 'IfMyKEyMW'],
['IbeZJFJMg', 'IbBKZUx^G'], ['Ir^iKmwio', 'Infi[eJZO'], ['IrFliNYGW',
'IbTHkuyYo'], ['IrTik~wIW', 'Irey{UXXg'], ['IzwyGuH[W', 'Id{JjFbXO'],
['I~DHLVgWO', 'I~KiKVgWO'], ['InFwinnhW', 'InFwifzlW'], ['IfvLWEOyG',
'IvmysCt?G'], ['I|yLKU_i?', 'It}H[UgI?'], ['IvOwcUCG?', 'IrQwcUCG?'],
['I~FkneKz?', 'IbRINF}ng'], ['IrMYneMi?', 'IzH]H]JgW'], ['IvHmxeIi?',
'Iv`jxeIi?'], ['IbE}\\}Iy?', 'IfRMzeXiO'], ['IrWmZ}}i?', 'IvM{HvLko'],
['Ijxz|VJig', 'IbnYMn}nG'], ['IrsKxEGiO', 'InoLWUGiO'], ['Iz{NlFyio',
'Irv]{mVCw'], ['IzskjNkjo', 'Izw|inYHW'], ['IbQGZ~WiO', 'IvEh^EKgG'],
['IrV\\HEJio', 'IrM}MEIWw'], ['IbW\\ZNIjw', 'IvVxkmGWw'], ['IfwHHUGw?',
'IvBg{CCAg'], ['IfQ^XFyZO', 'In[KzNgiW'], ['Inf{XFwYO', 'IrZHNFzM_'],
['IbHHhNiW?', 'IbHIhNiW?'], ['Ibh|HEi]_', 'IvDJwEKYw'], ['IvpNxEI[?',
'IzinhNGI?'], ['IrKMLEI[_', 'IdWMhEMy?'], ['IncLx^Jyg', 'Izjy[MJxW'],
['IrC[JNKYG', 'IjEyGuHgo'], ['IrFMXNGmG', 'IbQ]LUMNO'], ['IbFHJej]_',
'IbQ\\JFhMg'], ['IjA[Jfg^?', 'IjAkJfwN?'], ['IzLhxNhWW', 'IzhzHMxWW'],
['IvHzYF~gW', 'I~c~{EJJo'], ['IzD\\Meziw', 'I~VymENIW'], ['IvTHKegHo',
'Id{ghNBX?'], ['IrSmKEHIO', 'IhOitEMk?'], ['IzTw\\eIWW', 'IzEkYemiO'],
['IrDgMuz[O', 'IjMjYUJiO'], ['Izng^e}}W', 'Izfg^f}}W'], ['IjZKoFAGG',
'IbFYOEUGg'], ['IzY]rN\\Mg', 'IrY]zN\\Mg'], ['Irm\\[u?~w', 'IvfKsmVdw'],
['IfW[v]t~O', 'Ifwwrm|n_'], ['IjUKzUKi?', 'IjtKLUiM?'], ['Irsmzeky?',
'IvFGyMZ{W'], ['IbQGjMNnw', 'IvdkkuI{O'], ['IbxJjFihg', 'IjEwLnmWW'],
['IviNheIi?', 'Iz{lLNGI?'], ['IbXM|~]n_', 'IrVllm|Ww'], ['Inhll]yio',
'IrDZMF|~o'], ['Inhll]yio', 'Id{gx^Vzg'], ['IjC[ZVGgo', 'IbeLJFhM?'],
['IfEXhV]iO', 'IvhYLUjIO'], ['IjTKjfmjO', 'IjZ[jMYhW'], ['IbYWzNzwO',
'Ib{[pNt|?'], ['Iz^ijMmgW', 'Iz^nMUwHo'], ['IjQMxFY~o', 'IfIWxe]^w'],
['I~PNjN^ko', 'I~@j\\nn{G'], ['IfpGL~W\\G', 'If^lbuCg_'], ['IfrHhmi\\W',
'IjfLXnINO'], ['Ij}NJ^WJO', 'I~nKZ]WMG'], ['IbCLJNZZO', 'IbCLHnZZO'],
['Ijv{N^g]?', 'Iv~]NeLM?'], ['Ir`h|VIm?', 'IzLHymHWW'], ['IbPgl~N}O',
'InkzGF^gw'], ['IfaKnMNM?', 'Iz?NjFL]?'], ['IrfhKMGHW', 'IjWHrNci?'],
['IrtxlNJGW', 'IzTw\\eNWW'], ['I~\\Y|]HiW', 'Izmmmemko'], ['Izh^GMjXw',
'Izh]GNjXw'], ['IrDZMF|~o', 'Id{gx^Vzg'], ['IjFyNMhiW', 'IjFyNMjIW'],
['IbVgNeiho', 'IrCz[UxXG'], ['IvXz\\Epgw', 'InXz\\Epgw'], ['IrSI{cVUG',
'IrSG{sVUG'], ['IbYjxEig?', 'IzOnhEYI?'], ['Ib?yjeKiw', 'IrDYh]wGW'],
['IbgJLfWi?', 'IfCi|EGhO'], ['IbSiH}]y?', 'IrFjg]GwW'], ['IjvmleZn_',
'Iv^ilM]mW'], ['IbjxnfIi_', 'IrwyWnJXW'], ['IbjxnfIi_', 'IvWY~MshG'],
['Ib`WjEJiO', 'IjoGhMihO'], ['IbM}LmGhO', 'IbSZ|f[GG'], ['IbkMHeGwO',
'IbKMXeGwO'], ['IfYghUGio', 'IrdGo}EcW'], ['In]JhUMio', 'IrQ\\|fWmO'],
['Ir\\YlUGmO', 'InAM|]G}?'], ['IjsW~eMzO', 'I~LGYM|Xw'], ['IrTWXEYkW',
'IbOh[NWzO'], ['Iv@i\\eLWG', 'IbPIpMtlO'], ['IfPwJ]gXG', 'Il[zhEKw?'],
['IbxiZUIW?', 'IrE[{cUAg'], ['IbZG|FJ[?', 'IbCNhMk]O'], ['InEkXNYI?',
'Ir`KwdTrG'], ['IzxLLmMN_', 'IfziNmwM_'], ['Iru[{}WG?', 'Ivfl{kS?G'],
['IvWhWMWg?', 'IfwhWMWg?'], ['IbgI{mhj?', 'IbgIwmhn?'], ['IrwyWnJXW',
'IvWY~MshG'], ['IbDHkUxio', 'IbDj[FwMO'], ['InFgIFm{O', 'InFgIEm|O'],
['IfOIzMehG', 'IbWJvMchG'], ['I`K[CAsEG', 'I`k{C?sAG'], ['IbgMxeIm?',
'IfI[[U?}G'], ['IrSJ\\min_', 'Ib@Kn^m}G'], ['IbDgh]mig', 'IbDgju}i?'],
['IrVK~uMm_', 'Ifj]W}ymO'], ['IvXKnmJiG', 'IzDjzM[gW'], ['IbBGjeI~w',
'IzXMJFL]?'], ['InA\\hV[yW', 'InfXZFHN_'], ['Ibykx]GgO', 'Ij[IxEiiO'],
['IfVWlu[lO', 'I~Kj^VgWO'], ['Ijq]hUKgw', 'IzYygVHgW'], ['Ijq]hUKgw',
'IfXW\\e`lg'], ['Ijq]hUKgw', 'IbSlvMehG'], ['IbQ\\lU\\lO', 'Ibdl|Ehn?'],
['IfWH|EMjO', 'IvC[HNKyW'], ['IjWKlEHwW', 'Ib^GHEX[W'], ['IjQHxFYxo',
'IvgmHmNi?'], ['Ibw}|]\\gW', 'Iv]|IMi{o'], ['If}[~U]hW', 'Iv{Z[MX}w'],
['I~BWLvkzG', 'Ij}l^]UGG'], ['Iji[xMG{?', 'IvtISKVCW'], ['I~@yjMJXw',
'I~[NLmGxo'], ['Ir@ghM~wG', 'IjG|\\U{GG'], ['Ij}YlMWYG', 'IbWNtMdn_'],
['IzIIlN[zG', 'IrpZLFyNG'], ['IzIIlN[zG', 'I~cikeJNo'], ['IzIIlN[zG',
'IbTz]Ewjg'], ['IrjYxEI]_', 'If[NW}GlO'], ['IjCMhNKiG', 'IrJILEJMG'],
['Ifd\\HNGzO', 'IjqKJUZmO'], ['Ib`{HNKm?', 'IrSjHNoi?'], ['IrpZLFyNG',
'I~cikeJNo'], ['IrpZLFyNG', 'IbTz]Ewjg'], ['IziMN^nM?', 'IjyMN^nM?'],
['Ibu[^~XM?', 'Ivm[xvGMo'], ['IvdkNmGm?', 'Irs[gFG^w'], ['I~JXHN\\G?',
'IvC^sfl?G'], ['Ir\\kgFGYw', 'Irt{wEGWw'], ['IzYygVHgW', 'IfXW\\e`lg'],
['IzYygVHgW', 'IbSlvMehG'], ['IvCmLugYW', 'IbXGpmnio'], ['I~cikeJNo',
'IbTz]Ewjg'], ['IjCi|uHMW', 'IbDi{}HMW'], ['IjC}kuMxw', 'I~EmYEZ{W'],
['IfViINNzW', 'I~RxrNshG'], ['Iff]wEU^G', 'Ifv]wEQ^G'], ['IfXW\\e`lg',
'IbSlvMehG'], ['InO\\^FNGG', 'InOX^NNGG'], ['IrT{pMFg?', 'IrPmpmMg?'],
['IrUk|Ugi?', 'IzWmhUYI_'], ['Ij`iLnyiG', 'IvyGj]YwO'], ['Ij`iLnyiG',
'IduKhV`^o'], ['IzSn\\mI}_', 'Ijw|JFmhw'], ['Iz@[~uImG', 'Ij^Ghm]yO'],
['Ij@Kh]Iy_', 'Ibo[hE\\kO'], ['IbfKjuMjG', 'IjUgIem}o'], ['Iv]i^EG{O',
'In[mL]GmO'], ['IreIL][gO', 'IrQLlUMgO'], ['IreIL][gO', 'IrEh^EkgG'],
['IvyGj]YwO', 'IduKhV`^o'], ['IrQLlUMgO', 'IrEh^EkgG'], ['Ir{MlFMhO',
'IfpMLeMnG'], ['IbwH|UNhO', 'IjTHNEw}O'], ['IfB[|UGgO', 'I|O{hEkw?'],
['IbUgzvXgO', 'IjFJjEh]_'], ['IrT[JE~go', 'IvOWze]xO'], ['If[LXUXW?',
'IrIzXEG{?'], ['Ir{k|MGy?', 'Ivkk]E?|g'], ['Ibv^NnGZO', 'IzH~^EHhw'],
['IbPM^EgM?', 'IfGMgmJi?'], ['I~~k|vmm?', 'I~nl^m{jO'], ['I~yM^M}n_',
'Izw^zU^hw'], ['Ibe^jfXM?', 'IfzKZUw]?'], ['IbMI\\nIg?', 'IjEh]vGGG'],
['IzkZGN~wW', 'Izzhpncig'], ['IjFl^mwjO', 'IbW{t}||?'], ['IfTNkMwYo',
'IzDikFNJW'], ['InnHKemJo', 'IzDiLfZjO'], ['IzSgMMiwW', 'IrSgNMiwW'],
['I|El\\^?G?', 'Iv?N[ff?G'], ['IzZ~[tt?G', 'IzZ^]tt?G'], ['I~Il~EGg?',
'Ib{MxEI]_'], ['IzsLjUIi?', 'IzlGUtfAG'], ['Irol~MYxw', 'IbHY|]m~o'],
['IbOjHnY~w', 'Iz|k[uJYO'], ['IvXGn~}}_', 'InZMhm}yw'], ['IrDGh~Jm_',
'IvYINEyN?'], ['InHGjnijG', 'InHGjminG'], ['Ijc[HVGko', 'IbSMHmYgW'],
['IjoGhEhgo', 'IboipMFg?'], ['IfT]~EljO', 'Ibw]rMvz_'], ['IbWGhNZlO',
'IbtLKegJo'], ['IrhyxUGgO', 'IjOkLNGz_'], ['IbRG\\vWhO', 'IfRhZEwWO'],
['IzOKLM\\lw', 'IjxWHfmyO'], ['If_HxUJwG', 'IfgHxUHwG'], ['Ij@}NnK[?',
'Ih[NpeMy_'], ['Irk\\HngYG', 'Ivc\\LnGYG'], ['IrDKXNIMG', 'IbakjNHM?'],
['IrPM\\Eh}_', 'IfsJhFbZ_'], ['If`]\\ekM?', 'Ibd]\\ekM?'], ['IjhGNUJNO',
'Ij`GNUJnO'], ['Ij\\klv}m?', 'IzXklv}m?'], ['Ib@[LuzN?', 'IbkMKmwiW'],
['Ib@[LuzN?', 'IrNHKMwiW'], ['IbqXJMHmo', 'IvZ[RM@Gw'], ['IbkMKmwiW',
'IrNHKMwiW'], ['I~XnjmGjO', 'InxyznMg?'], ['I~W\\I^WXw', 'Ibvhyejko'],
['IrlwwEGIw', 'IzLlgV?go'], ['IvDWwE]lW', 'If{]]U?]G'], ['IzLIi}MyW',
'Ijvhke|Ho'], ['IzgzHN~WW', 'IzNxLM{jO'], ['Ib^mJeigo', 'Iz@y[U\\Ww'],
['IrUiYUmgo', 'IbMiYUmwo'], ['InoL~eGi?', 'Ij@hjN[Wg'], ['IbWNzFKi_',
'IjRiHNwwO'], ['Ib}MzUIi?', 'IrHNxUii_'], ['Ibc}\\mIyo', 'IfqWjnI\\W'],
['IbpiJmYm?', 'IjUIlFMhO'], ['IbpiJmYm?', 'IvTwIMigo'], ['IfDmLuY~?',
'IbW|jUYww'], ['IfDmLuY~?', 'IjO|jUYiw'], ['If?MHmYjw', 'IfALxEyxO'],
['If~ZLUjgW', 'I~EwyMn{O'], ['IrkMHeGwO', 'IbKNXeGwO'], ['IvQX|VGiO',
'IrL^HNgYG'], ['IjUMx]inW', 'IvFLX]Xyw'], ['IjUMx]inW', 'IvgzM]xYW'],
['IjUMx]inW', 'I~Uy{eJjO'], ['IjUIlFMhO', 'IvTwIMigo'], ['IrsG|EXgw',
'IzQXzMMg?'], ['IbyyXFWko', 'IjOl[N[jO'], ['IjOKNN|ko', 'Ifk}WFJio'],
['IbtWH}ZgO', 'IvEx]EkgG'], ['IbW|jUYww', 'IjO|jUYiw'], ['IvPgHEKYG',
'IzFGGEWLW'], ['IvFLX]Xyw', 'IvgzM]xYW'], ['IvFLX]Xyw', 'I~Uy{eJjO'],
['Ib{JxUIY_', 'IzwlXUwI?'], ['IjhMXELW?', 'IjhLXELW?'], ['In`kX^I[?',
'In_kX^i[?'], ['InQI\\Mi[?', 'IjRI\\ehM?'], ['IjTknVnMO', 'Iz^Jj]JgW'],
['IfbGlvI}o', 'IfvGlvI]_'], ['IbRGn^InW', 'IvG]zEXkw'], ['IbQMLuN^?',
'IbQMLe^^?'], ['IfAHnEKMO', 'IbP[{UggG'], ['Ijq]JFZN_', 'IrlX]ehIw'],
['Iba|NmHMo', 'In{m[UgWW'], ['IbPI[]~G?', 'IzlJTsK?G'], ['IrhjY]hG?',
'Iz~KhEeG?'], ['Ij\\jKNYzO', 'IrZzh]HhW'], ['IvGNh}ni?', 'IvGMl}ni?'],
['Iz]^KN^Nw', 'Ir^^VNvMg'], ['IrVylM^~w', 'I~ty~fT\\W'], ['IvgzM]xYW',
'I~Uy{eJjO'], ['Izl~GMxWW', 'IdvjlNDZO'], ['IzLL]FyIO', 'If|n[EgXO'],
['I~Dw{eM[W', 'IzF{K]M[W'], ['IfvxMnj|o', 'Izu^rNvHw'], ['Ifehj]~lo',
'I~}WVM\\Lw'], ['It\\gxN^~?', 'IrRIr}nyg'], ['IvDHuEn?G', 'IzSXUEv?G']]
WARNING: Output truncated!  
full_output.txt



[['IbQGjMM}g', 'IfEiMMkZO'], ['InPHx}ii_', 'IrthkNyGW'], ['I~hKjniiG', 'IrVMlmjgW'], ['IvhGzM]iW', 'IrHWnnMm_'], ['IfQkluGhO', 'IrpK{EFeG'], ['IzPkxmGkO', 'IvxXgFIgW'], ['IbtWHeW|O', 'IvgHHFiWw'], ['IvqL|eWgO', 'InBW[U?~w'], ['IbR{J]ZjW', 'IbR{JU^jW'], ['IbR{J]ZjW', 'InF\\kewyo'], ['IbR{JU^jW', 'InF\\kewyo'], ['If_JHFIYo', 'I`WG`vswg'], ['IrMJ|^W]g', 'Iv\\NtMdhg'], ['IjPIz^mWG', 'IvONwEYno'], ['IrcNLEI]?', 'I|OKxEky?'], ['IvcLJNGNO', 'IfJJLEjm?'], ['InSMXnIjO', 'IvSgh^fZ?'], ['IbOlxNhI?', 'IfEg}E?ww'], ['Ib@M\\UhN_', 'Ib@M\\UhNO'], ['IbHGlmJNw', 'Ij\\J{egHo'], ['IjRZJNL]g', 'IzxzINJWW'], ['Ir[\\i^w^W', 'Iv\\myNZgW'], ['Ir[\\i^w^W', 'I~likeJ~O'], ['IrVHmMxyW', 'IzvhIejko'], ['Iv\\myNZgW', 'I~likeJ~O'], ['IzThyN\\gW', 'I~hZLEJjo'], ['Izw^~V~hw', 'I~~[~~Xig'], ['IvdH[Eg|O', 'IvDL[Eg|O'], ['IbKmNvnJO', 'Ij}k]EJ}O'], ['IvfkkEI{o', 'IzYlxMcm?'], ['I|ynXEAi_', 'Ix{NxFiI?'], ['IvImgEiG?', 'IrgmoEmG?'], ['IzQgjF|nW', 'IbDG|}nno'], ['IrSKjuNm?', 'IfIWNeNm_'], ['IzGLjf}iG', 'IfENze}M?'], ['Ibo[jUYh?', 'InDHKugWW'], ['Ib?JHeWmW', 'IbsWpmEg?'], ['Ij{mX}]yO', 'IrC~}UZxg'], ['IbXGnNM~_', 'Id^YhNX|?'], ['I~Tg|]Ggo', 'IbwNlewiW'], ['IbsNlEwiO', 'IzS{|NGI?'], ['IblMjuGiO', 'IblNhuGiO'], ['IblMjuGiO', 'IzG]zNgI?'], ['IblNhuGiO', 'IzG]zNgI?'], ['IjYj|NYio', 'InvH]Uwjo'], ['IfXh^uIXg', 'IvlHLmN]?'], ['IfAWL]wwW', 'IfAWH]wxW'], ['IzrwhN{Xg', 'IvmlL^GzO'], ['Ifr]lmIwW', 'Ir~YZ]J[?'], ['IfC\\XNHnW', 'IzRKtmei_'], ['Ij|MlUi]_', 'IjlNlUi]_'], ['I~eK^EW}O', 'IrXyIF~gW'], ['IvW]l^YlW', 'I~tzkFJJW'], ['IzD[WFGYw', 'IzD\\WFGWw'], ['IzDim^WIW', 'IrDik^xIW'], ['Iz|ZI^|wW', 'Iz~ZIN|wW'], ['IbNHKuw]o', 'IfujKFLIW'], ['IjEyMEhiW', 'IjEyMEjIW'], ['I~AIwEAhG', 'IzAIwEAxG'], ['Irw[[U?{G', 'Irg\\[U?{G'], ['IvwivEuG?', 'IfXjvEfG?'], ['Id}llUcG?', 'Ir{GS~t?G'], ['IbhyjfMi?', 'Ibgyjf]i?'], ['IbQYjeMj?', 'IbQIjeMj_'], ['IviHnEMi?', 'IfiLnEMi?'], ['IreGjMMiO', 'IrRGx]XgO'], ['IrskjMYxo', 'Irsgj]Yxo'], ['IjOiHm]zO', 'IrgzIMNWW'], ['Ivlwl^i}?', 'I~J^WnyiO'], ['IvN^XeXgW', 'Iv\\KYNYww'], ['IvN^XeXgW', 'IbxW|}`mg'], ['Ibc]LVWmO', 'If?j|elWG'], ['IvWKhUhiO', 'IrD|lUGgO'], ['IjQYnVlgO', 'I~Yg~FWgO'], ['IbQyxfWhO', 'IjoL{NWhO'], ['I~@JHMKWw', 'Ij?mNe\\[?'], ['If@Jz}WwG', 'IjQKZfg~?'], ['IjsKjNHiW', 'Irq\\ZFhM?'], ['Ib`KlmM]o', 'IbYMNFyM_'], ['Iri|JF|M?', 'Ity[|^@Z?'], ['IjiKN}ZN?', 'IzZyiVHgW'], ['Ir]|^MHM_', 'IjQzJnhN_'], ['IzUKZEwM?', 'IfCgIMZnO'], ['IvA]ZmkM?', 'IvANZmkM?'], ['IrT{wEGwW', 'IjYKzMUg?'], ['IvNn}^MgW', 'Irn~g^|WW'], ['IvfyzmWkW', 'Iv|YY^XiW'], ['Iv\\KYNYww', 'IbxW|}`mg'], ['IrWyhULhW', 'IzciKeJnO'], ['Ix{~}F{G?', 'I~JXT~|?G'], ['IvohU^GG?', 'IvsISsu?G'], ['Ij@Kje[nG', 'Id[GhvTxG'], ['IbrWjNZzg', 'IftghF|~O'], ['IzKMHexy?', 'Ib]MzMFg?'], ['InpmX~mi_', 'Izfg^fJyW'], ['Inn}LuYiG', 'IbP{nv^mO'], ['IbeyXeIy_', 'IrUkhM\\gO'], ['IbLGj]y}?', 'IfGiKnxyO'], ['IbLgj]i~O', 'Ir[[JFymW'], ['Ivh[jMjiO', 'IbVXke{yo'], ['IjFYhNJkw', 'IjXGpmnyo'], ['IbSLhU]hW', 'IjYg~FWgO'], ['IbSLhU]hW', 'IlRGlNBNO'], ['IjvGjNIhw', 'IrXlLfMMg'], ['IfVGxMXlO', 'IbX]JEmwW'], ['IjYg~FWgO', 'IlRGlNBNO'], ['Iz[\\JMMhW', 'IzLik]NgW'], ['In?JXeh{_', 'IvRWHNWYG'], ['IfQgN~XwW', 'IfON|UY{g'], ['IfQgN~XwW', 'Ib|{zuGm?'], ['IfuMlMW]g', 'IrjYH]ngW'], ['IbsGnEY]O', 'IfSX\\VJGG'], ['IfON|UY{g', 'Ib|{zuGm?'], ['IjSKxNGiG', 'IjG\\HnGZ?'], ['I~KNLnWjO', 'I~KNLNWzO'], ['IbFHjejN_', 'IbFHJejNo'], ['IfQMZf{m_', 'IfSk~MuhG'], ['IrG}ZElM_', 'IzTJkMJWW'], ['IzHhh^gG?', 'IzGhh^iG?'], ['I~wKxm\\G?', 'IbNzoFOjg'], ['Ib{IN}Mi?', 'Ib{NYmMi?'], ['Iv[^M~WNw', 'Iz^XnMxyW'], ['IzFXwEGlW', 'IzF\\wEGhW'], ['IfMygEhiW', 'IjmgYEi{O'], ['I~fNWEUIg', 'Ir`ltv^?G'], ['I|qK\\Eai?', 'I`{mXVgI?'], ['I|Xgy]`G?', 'Ix[Y|UcG?'], ['Ir_w~u]h?', 'IzvGhm\\gO'], ['Ir{JhuYi?', 'Ir[NlEI]_'], ['IreMjeIi?', 'I`ulLNoi?'], ['InXjHvmy_', 'Ir}[NUijW'], ['IrOj\\mYi?', 'IzFgKeY[W'], ['IjPzhm]j?', 'IbIzKm}jG'], ['IbciLmImO', 'IbciHmImo'], ['IrLLHEYi?', 'IrDLXEYi?'], ['Ir@Ll]mm?', 'IfHHNUi]o'], ['IbK{LvKgw', 'IjEwjeMiW'], ['Ifdw\\VigO', 'IfDw\\vigO'], ['IrvglEGkO', 'Ir@GjMnwG'], ['Ivq|jmGko', 'Iv~^gEYGw'], ['IvsK|EXgw', 'IzQ^zMMg?'], ['IzOLhM~{o', 'InuMxNwWg'], ['IbXkhNWxo', 'Ij\\HKMyJo'], ['Iv[{JeMhW', 'IvW\\mN[HW'], ['I~z~j}Z|W', 'I~z}~Mzno'], ['Ir]|JMZhw', 'Irz\\rMxig'], ['IrbgjMJw?', 'IragjMjw?'], ['If]I|MWyG', 'IbF\\[Ug]w'], ['Ib?HhN~Wg', 'Ib?Hhn~WG'], ['InGN|EG{_', 'IzWzzMCg?'], ['Irh[lE]M?', 'IjmmHUHgo'], ['IjaiNFwmo', 'I|W]xN@^?'], ['Ib]MLUI]?', 'IvOKw]WJo'], ['IfAKzVLN?', 'IfxYLEJMO'], ['IvOg\\nhG?', 'IjC\\GEMxg'], ['InOZ{MWjO', 'IjRKxmcio'], ['IrFIk}GkW', 'Iz?j[VYMG'], ['Ifsgn]zgo', 'IfSwjMzlo'], ['IzBw\\~sXW', 'IjBw\\~s\\W'], ['I~yXtmFg?', 'Izy\\tmFg?'], ['IbXKlE|G?', 'IjsJkmcG?'], ['IrXLxE[G?', 'I|QkYm`G?'], ['I~c{zeKiG', 'I|vJhF`Xo'], ['IziJjEIi?', 'IziKxEI{?'], ['IzpwjNYxO', 'Ir}kMemio'], ['Inhgh]yio', 'Id{gx^Rx_'], ['Iv{KlUKhO', 'IbFiIM^hW'], ['I~UllMigW', 'IrrKn]ZhO'], ['IbwHzeWgO', 'IboLzeWgO'], ['IvSG\\uWiO', 'IfwG\\uG{O'], ['I~U^XEI{o', 'InFiGE~xw'], ['IrTWJEjwW', 'Ib@MLfmMo'], ['IjY\\jEYlw', 'IbW[pnlzW'], ['IfBWzFNWw', 'IrTgLNNwW'], ['IfcMhFIYO', 'IrAG}FTeG'], ['I~?NjNnXw', 'If[x~u?}w'], ['IjZwjM~ZG', 'Ijt~Z~gY?'], ['IbxHLE]N_', 'IbpHLE]n_'], ['Ir|n|Uymg', 'If{[v}t~O'], ['IrZhJE~mg', 'IzW^rNdxO'], ['Iv]\\jMZnw', 'IvY{rm|~G'], ['Ir~lIMGiW', 'IbDHNNl]W'], ['IrFW{mXxW', 'IrFwNu][O'], ['IrUgINlGW', 'IrUGJNlGW'], ['Ivci|UHKO', 'Irkm|EHKO'], ['InSgIEIio', 'IbOGrMfx?'], ['IrOISdn?G', 'Ira[[CCeG'], ['IzUGneLm?', 'IbD\\KMxNo'], ['IrWIzeKiG', 'IrGIzeKig'], ['IbXgxEii_', 'Iz]GSduAG'], ['IjZIlEIiO', 'IvXKjEIiG'], ['Iffxj^Zi?', 'I~DLMFn\\o'], ['Iv[wneGxO', 'Ir[wnuGxO'], ['IjsN|EwiO', 'Iz\\LxNLI?'], ['IjsN|EwiO', 'IvpW{EVuG'], ['Ij{LhmyhO', 'Iryg~NWgo'], ['IbQGHuWgO', 'IrQWPUIGG'], ['InZ[jFYhW', 'Izw\\yNYHW'], ['InZ[jFYhW', 'Id}IhNX|W'], ['IvS\\jf}hW', 'IvJKNUZ~o'], ['Ir@ihN~wG', 'Iv{mZ]GM?'], ['IbgIzEY[?', 'IbWLhNhI?'], ['Ij|mZ]I[?', 'IzBN~FM[?'], ['Iz\\LxNLI?', 'IvpW{EVuG'], ['IjJWZmZ^w', 'I~kmkVHmw'], ['InB]nF]nW', 'I~nyNUHlo'], ['IvB{nmG~_', 'I~B{NmG~_'], ['Ib[xIN]G?', 'IpSLvE^G?'], ['IbRjLN{ho', 'Iz?y[^nWW'], ['InNZWmymO', 'InVi{vhWW'], ['I~U[GEwIw', 'Ir[kh~?go'], ['Izw\\yNYHW', 'Id}IhNX|W'], ['IvfmgEgiw', 'Ir{{p^Mg?'], ['IvfLwFMXW', 'IvdLwF]XW'], ['I~DGwmZgW', 'I~DGwNZgW'], ['I~}~imz^w', 'I~Vnl}n~o'], ['Ivw]wUHlw', 'Ifugt}dlG'], ['Ijc{]e?jG', 'InHW[^bGG'], ['Ivu[uESG?', 'Ivs[ueSG?'], ['IrOMtMeh?', 'IrOMvMch?'], ['If{[rM|zO', 'Ifw[r]|zO'], ['If}]WEwG?', 'I~RYWFUG?'], ['IjOKje]mG', 'IjSKje]iG'], ['InOG~eKi?', 'IjbKLUiM?'], ['Ijfy~fJiW', 'Iv[^m^wJW'], ['IzL~\\uyiG', 'Ibx{N}^kW'], ['IjcmL}]yO', 'InLXzMMiW'], ['IjRWHN\\iW', 'IjOW~]nGG'], ['IjYGxFYgO', 'If_i|eGWg'], ['IzQJxFYxO', 'IjQJxFY|O'], ['InR]hN{ko', 'IvtKyM]kw'], ['IbSMHMZiW', 'IjDXKNkMO'], ['Inx[HMYgO', 'Ib@MLmk}_'], ['In}WLu]}O', 'IvGIL}~jw'], ['Iz?nhNXWg', 'InIj|EG{_'], ['Ib@HhmZWG', 'IzZWpFAGG'], ['IjBxneH\\W', 'Ibpm\\^HYo'], ['IjBxneH\\W', 'Ir`][]Mdw'], ['Ibpm\\^HYo', 'Ir`][]Mdw'], ['Ij@nLemNO', 'IfdX~egHo'], ['IrbM\\eiM?', 'IrhyHUhgW'], ['IbQGJM}G?', 'IfCgVNHG?'], ['IfgJkmGwO', 'IrOxp]Mg?'], ['I~QxGNhxw', 'I~cm\\uhIW'], ['InHZNEJZo', 'IzCzLmJjO'], ['IjmjHUhgO', 'IjMjLUhgO'], ['IzFykM^xo', 'IzTz^VXXG'], ['InT|]Eo~G', 'InT|}EonG'], ['Id{yuU}G?', 'Itq}mUuG?'], ['Id{mvE}G?', 'IvmmsdV?G'], ['I~aK~EIg?', 'IzWhH^wGO'], ['IfKNXugiG', 'IfCNxugiG'], ['IfpiHumy_', 'IbYwzMywO'], ['IbXiHmniG', 'IlTghNd^?'], ['IbCmxmI}o', 'IbPWxmc~g'], ['IbDihmm}G', 'IvwWzeNgO'], ['Iv_mhmYi?', 'Iv?mxmYi?'], ['InUyHmI~O', 'IrgZ\\]JyW'], ['If`GneIj?', 'Ib`GjeInO'], ['IbfnXUIgO', 'IbBiNNhMO'], ['Ijd{JVGio', 'IfC{HVjko'], ['Iv\\Jx]GhO', 'In[z^EFGG'], ['IjyKhMiiO', 'IfDiKuLJW'], ['InUGlUMho', 'IjQX^MXM_'], ['InUGlUMho', 'IjRXNEZM_'], ['IfpGl][ko', 'IfpGh][mo'], ['Ij^wxFYwO', 'Inq[hMw{g'], ['IjPLLN{{w', 'Ir]]~E]M?'], ['Ij[{JFYwW', 'IbukMumgo'], ['If{wzUMgO', 'IbBW|^MNG'], ['Ir@gjmkWG', 'Ir@GjmlWG'], ['IfNWjMG]G', 'IzfgKEIiw'], ['IzPIZFkW?', 'IpSGV~HgO'], ['IjhhLEm]?', 'Ib[I[}wiO'], ['IjhhLEm]?', 'IjChKfngW'], ['IrBJNEnN_', 'IfMwNEMmW'], ['IjQX^MXM_', 'IjRXNEZM_'], ['IrQHLNYG?', 'IjQhoEKHg'], ['IjGxjMMG?', 'IbHxjMiG?'], ['IjPJKNxhO', 'IbEyIE^xO'], ['IfM}Gmyi?', 'IrFkKE]\\W'], ['Ir^IKmwyo', 'IzDgy^[iW'], ['Ir^IKmwyo', 'Indi{eJZO'], ['Ib[I[}wiO', 'IjChKfngW'], ['Irl{wEGIw', 'Ir\\gwFGYw'], ['Ir\\il}WiW', 'IjtN]MwjO'], ['IzDgy^[iW', 'Indi{eJZO'], ['IrnZINxWW', 'IrtNNNwIo'], ['Iv{]i}jhW', 'If[ymNmxw'], ['IbG[WFG]O', 'IjCh]EIGG'], ['I~|X}Ehiw', 'Ijriv}lig'], ['IzFwKeJWW', 'IrUiYUigo'], ['IbeiiEZjW', 'IbzKpmcio'], ['IrUh^VJGG', 'IrUj^FJGG'], ['I|{GHEgG?', 'Ix{GHFgG?'], ['Ifuk|UGi?', 'IzOnhEyI_'], ['IjiLjEgg?', 'IjJXPMeGG'], ['IvoNnEIg?', 'IfoN~EIg?'], ['IjCgzm~n_', 'IbY{hm{mw'], ['IrcNjuKiG', 'Ib[JHNYjo'], ['I~_I\\egi?', 'IzYGHnwGO'], ['IzflxE]zg', 'IjrnXNjyo'], ['IzPH|MIi?', 'IjpH|MIi?'], ['IrPGhuMm_', 'IbQGtncm_'], ['IzmIxEJkW', 'IzEmzVKM?'], ['IzmIxEJkW', 'IfU\\NUH]_'], ['IzmIxEJkW', 'IjHIKnxnO'], ['IzOIxUKxO', 'IrLIgNgYW'], ['IfWGlM{gW', 'IfWGl]kgW'], ['IfWGlM{gW', 'IbSMhMYwW'], ['IfWGl]kgW', 'IbSMhMYwW'], ['I~jgne{wO', 'IfBW|^^NG'], ['IfOGN~XgO', 'IvRwGM[hO'], ['IfW{jM}ho', 'Iv@jl^ym?'], ['I~IkxEkYG', 'InuLtMFg?'], ['IvIl|}G{o', 'Ib\\z}V^GG'], ['InpnLE]n?', 'IzQkJ}XnG'], ['IzEmzVKM?', 'IfU\\NUH]_'], ['IzEmzVKM?', 'IjHIKnxnO'], ['IvIKjFHM?', 'IdsGxVBXO'], ['IfU\\NUH]_', 'IjHIKnxnO'], ['IrE[NEwm?', 'IvKjMFgWO'], ['IjQh[MgG?', 'IrPh[MgG?'], ['IvAK[]GG?', 'Iv?N[cE?G'], ['IzOiGF\\GO', 'IzOiGE|GO'], ['IrlwgEGgw', 'Ib\\lgV?go'], ['IrVL{MiMw', 'IvVLvMehG'], ['IzZyg]HgW', 'IfXW\\e`mw'], ['InekiEMjO', 'IfPKpmcno'], ['I~mkmeIiW', 'I~ek}eIiW'], ['IrqG{F^eG', 'Ir_W{n^EG'], ['IfH[jEGh?', 'IbDKnMGh?'], ['I~CJ\\eGi?', 'IjpKXEii_'], ['Iz|}\\}yiG', 'Iz]^x]ilw'], ['IjD}|}]iG', 'IvHLl^y}_'], ['IntiLeiiG', 'ItsGjVb^O'], ['IbDiHfIy?', 'Ib@glNIj?'], ['IbCyH}y~W', 'IryYN]xIW'], ['IblK|]NyG', 'IjviInmgo'], ['IrHInuny?', 'Iv^G]NKgw'], ['IrHInuny?', 'Iv\\G]NKww'], ['IbFIlUYgO', 'IjUiGUHho'], ['Izm]hUHgW', 'IzfGYMWlw'], ['If]khuGhO', 'IrpW{EVeG'], ['IjPYjU{gw', 'Ibw{lmKkW'], ['IbYN|EIho', 'IvqktMcm?'], ['IzPKhM[ko', 'IjPKlM[ko'], ['Ib[}h^wgW', 'I~LX]EhIw'], ['Irs^hmWhO', 'I~PZHMLWw'], ['Irs^hmWhO', 'Iv\\NkMGiW'], ['If?[hNLYg', 'IfJG|EImG'], ['IfL{^EImG', 'Iba\\jFhNg'], 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'IfI\\LVggO'], ['IvjjLuiig', 'If]WhNz|G'], ['InHIlNi}?', 'IjJJWmyio'], ['IzHL|MIy_', 'IzHJ|MIy_'], ['IzJWzfIjG', 'IriJlNW^G'], ['InNm\\UYgO', 'IbBW~VZNO'], ['IfEiXMGxO', 'IfCiXMGzO'], ['IbQkhUGgO', 'Ir`G{cDEG'], ['IzO|xuGhO', 'Iv{ZWEK[W'], ['IfWWlE]hO', 'IjDhME{iO'], ['IzrGhMyho', 'IjcYhuMww'], ['IbU\\J}ihW', 'I~Kmg~GwW'], ['IbU\\J}ihW', 'IbRkpnkn_'], ['In{WLe~{W', 'Irf}HNW~g'], ['IjI{xMG{?', 'IrtIUKVCW'], ['Ib@jjMw[g', 'IzygIf\\GO'], ['IzjmLUL~?', 'Ij~hKMIzw'], ['IfBGlvNNO', 'Iz`y\\VJWG'], ['IbiXJ^XM_', 'IbiXJNxM_'], ['IvVHm]wyW', 'IfUMx]l~?'], ['IvxZYmXWW', 'IrmzJMXwW'], ['IrT|Me|Iw', 'In[ymNigw'], ['I~\\jMVgWO', 'I~LjNVgWO'], ['I~Kmg~GwW', 'IbRkpnkn_'], ['IrnnYUJiO', 'IbEyyEZ~o'], ['IzUnNemgo', 'Izrwpncz_'], ['I|Xgz]`G?', 'Ix[Z|UcG?'], ['IzPwjE\\mO', 'IbIwNezm_'], ['Ivel~UMi?', 'Ir}J\\UHiw'], ['IbNnLeImG', 'I~DikMWJw'], ['IfDG|EJjO', 'IrBiLEJMg'], ['I~JhzfizG', 'I~\\In}NgW'], ['I~JhzfizG', 'I~nmkUjmO'], ['Iv^klUGgO', 'IfPWNuLXW'], ['IbhhjEKwO', 'Ib`gL~I[?'], ['Ifo{zEMgO', 'IrI\\ZfGIo'], ['Ifpn\\eGWg', 'IbP[Lm]NO'], ['Ibe~JFlM?', 'IbHMgnl~?'], ['Ibe~JFlM?', 'InSz]EojG'], ['IbHMgnl~?', 'InSz]EojG'], ['I~\\In}NgW', 'I~nmkUjmO'], ['IvTim}gwW', 'Irtim}gwW'], ['IrgYY]JYw', 'IrgY]]JYW'], ['Ir]]gUHhW', 'IvSgzMigo'], ['IfLY\\EjMO', 'InuGzMchG'], ['IfKz[Fxiw', 'I|PI|Fj~?'], ['IjRw[]t\\W', 'IbuKv}dlO'], ['IpuKpUGg?', 'ItYM[EAG_'], ['IzZ|xECx?', 'I~{HpVmG_'], ['IvLwtV~?G', 'IzZLTf~?G'], ['I~{IVcCAG', 'Iz{JVcCAG'], ['IjGMjfK}G', 'IrQM~eMM?'], ['IbGIje[jw', 'IfDHX]G|g'], ['IbQGjMN~?', 'IjEmYEi{O'], ['IbONheYm?', 'Ivg\\[U?XG'], ['IfoN|fYi?', 'IzOY^VnGG'], ['IruNJeIi?', 'Ir}GxmWgO'], ['Ij?ijm]yG', 'IfhJj^Ii?'], ['InhhlNi}?', 'IbxmrNd|?'], ['IbqXlvWnO', 'IznXKngHo'], ['IfcXxvXlO', 'IbPKLmM~w'], ['If{MhEhiO', 'I~CH]V\\GG'], ['Ifjgjm[xO', 'Ivd|KMwio'], ['Ifjgjm[xO', 'I~dh^UgHo'], ['IzW~h^ZgW', 'IrDZMF~}o'], ['I~tWHeIgO', 'Iz|WHeIgO'], ['I~?m|f|XW', 'Izdjw}G|w'], ['IrWH\\EY}?', 'IrOH\\EY}_'], ['Ib`m\\^HYo', 'Ir`Y[]Mdw'], ['IrEKk]GG?', 'IvQ[OE?MG'], ['Ir[JKNYxW', 'IrUiImngo'], ['Ir\\i~M^iW', 'Ijvl]ej{o'], ['Irnm}m^{W', 'IfT~]Vnno'], ['IjTHKewYo', 'IbTHKuwYo'], ['Ivd|KMwio', 'I~dh^UgHo'], ['If\\LkNwIo', 'IbOnp]llG'], ['IjC~{UIwO', 'IvWjtMchG'], ['IjE\\?EWlG', 'IvNGOEWgg'], ['IjfHOEkIg', 'I~@hS{k?G'], ['I~YxnNIG?', 'I~YwnNiG?'], ['IrxgzN]xO', 'IrpgzM}xW'], ['I~`yLmYmG', 'IjakZUzMw'], ['I~`yLmYmG', 'Ijeg]VJ{w'], ['I~FinMZlW', 'IzFinNZlW'], ['IboHxUhio', 'IrDNgEWMw'], ['IfO\\hU[lO', 'IbPGpmejw'], ['If{WxMzhO', 'IzqNINyJO'], ['Ib@IhEhlO', 'IjOY\\eKGG'], ['IfFLXFwZO', 'Iro]rMdl?'], ['IfgHhEIWo', 'IjCKx^GI?'], ['IfGWXUw]G', 'Ifi|HFGHO'], ['IrHlZEiW?', 'IrWhZEmW?'], ['IbqGJmH~O', 'IzGKxN}I?'], ['InUX^eHM_', 'InQX^uHM_'], ['InA[JMXMO', 'InAKJMXmO'], ['IjakZUzMw', 'Ijeg]VJ{w'], ['IzZwGFWHW', 'I~|ITkCAG'], ['IrV\\i]H|W', 'Irg^g]z{W'], ['IvYyh]LhW', 'I|SljFfZO'], ['IfCmLugWW', 'IbUmIUZgO'], ['InfXoEagg', 'I|XMI]tG?'], ['IzSYmEMG?', 'IvDHvKd?G'], ['IryWjELm?', 'Ir_y\\UNWG'], ['IrQGn^Ln?', 'IfXhzmci_'], ['IjVIzvMy_', 'IbeXjF~Ng'], ['Iv{NHvhy_', 'IjDhj]~[g'], ['Iv{NHvhy_', 'If}NNnxg?'], ['Iz\\HHEYi?', 'IzlHHEYi?'], ['IzlKHEm}?', 'IvFIWEk|W'], ['IjuyXFJhw', 'IvQWZv]xO'], ['IvcixeGhO', 'IjWLL^KI_'], ['Ij_XxVGjO', 'IbPKNmMMG'], ['IfYK|MIho', 'IzelIUigo'], ['Iz\\|JF~gW', 'IzZ~NFj]?'], ['InAHxF[Yg', 'I~DWWEYhw'], ['In?wJVHZW', 'IziG]nFAG'], ['IrAghNKXG', 'IrOIWEW|o'], ['IfIGlMGZG', 'IjDgMEMIW'], ['IzYIlN]YG', 'IjcyG~H|o'], ['IjDhj]~[g', 'If}NNnxg?'], ['IjBiNei]O', 'IfMyKEyMW'], ['IbeZJFJMg', 'IbBKZUx^G'], ['Ir^iKmwio', 'Infi[eJZO'], ['IrFliNYGW', 'IbTHkuyYo'], ['IrTik~wIW', 'Irey{UXXg'], ['IzwyGuH[W', 'Id{JjFbXO'], ['I~DHLVgWO', 'I~KiKVgWO'], ['InFwinnhW', 'InFwifzlW'], ['IfvLWEOyG', 'IvmysCt?G'], ['I|yLKU_i?', 'It}H[UgI?'], ['IvOwcUCG?', 'IrQwcUCG?'], ['I~FkneKz?', 'IbRINF}ng'], ['IrMYneMi?', 'IzH]H]JgW'], ['IvHmxeIi?', 'Iv`jxeIi?'], ['IbE}\\}Iy?', 'IfRMzeXiO'], ['IrWmZ}}i?', 'IvM{HvLko'], ['Ijxz|VJig', 'IbnYMn}nG'], ['IrsKxEGiO', 'InoLWUGiO'], ['Iz{NlFyio', 'Irv]{mVCw'], ['IzskjNkjo', 'Izw|inYHW'], ['IbQGZ~WiO', 'IvEh^EKgG'], ['IrV\\HEJio', 'IrM}MEIWw'], ['IbW\\ZNIjw', 'IvVxkmGWw'], ['IfwHHUGw?', 'IvBg{CCAg'], ['IfQ^XFyZO', 'In[KzNgiW'], ['Inf{XFwYO', 'IrZHNFzM_'], ['IbHHhNiW?', 'IbHIhNiW?'], ['Ibh|HEi]_', 'IvDJwEKYw'], ['IvpNxEI[?', 'IzinhNGI?'], ['IrKMLEI[_', 'IdWMhEMy?'], ['IncLx^Jyg', 'Izjy[MJxW'], ['IrC[JNKYG', 'IjEyGuHgo'], ['IrFMXNGmG', 'IbQ]LUMNO'], ['IbFHJej]_', 'IbQ\\JFhMg'], ['IjA[Jfg^?', 'IjAkJfwN?'], ['IzLhxNhWW', 'IzhzHMxWW'], ['IvHzYF~gW', 'I~c~{EJJo'], ['IzD\\Meziw', 'I~VymENIW'], ['IvTHKegHo', 'Id{ghNBX?'], ['IrSmKEHIO', 'IhOitEMk?'], ['IzTw\\eIWW', 'IzEkYemiO'], ['IrDgMuz[O', 'IjMjYUJiO'], ['Izng^e}}W', 'Izfg^f}}W'], ['IjZKoFAGG', 'IbFYOEUGg'], ['IzY]rN\\Mg', 'IrY]zN\\Mg'], ['Irm\\[u?~w', 'IvfKsmVdw'], ['IfW[v]t~O', 'Ifwwrm|n_'], ['IjUKzUKi?', 'IjtKLUiM?'], ['Irsmzeky?', 'IvFGyMZ{W'], ['IbQGjMNnw', 'IvdkkuI{O'], ['IbxJjFihg', 'IjEwLnmWW'], ['IviNheIi?', 'Iz{lLNGI?'], ['IbXM|~]n_', 'IrVllm|Ww'], ['Inhll]yio', 'IrDZMF|~o'], ['Inhll]yio', 'Id{gx^Vzg'], ['IjC[ZVGgo', 'IbeLJFhM?'], ['IfEXhV]iO', 'IvhYLUjIO'], ['IjTKjfmjO', 'IjZ[jMYhW'], ['IbYWzNzwO', 'Ib{[pNt|?'], ['Iz^ijMmgW', 'Iz^nMUwHo'], ['IjQMxFY~o', 'IfIWxe]^w'], ['I~PNjN^ko', 'I~@j\\nn{G'], ['IfpGL~W\\G', 'If^lbuCg_'], ['IfrHhmi\\W', 'IjfLXnINO'], ['Ij}NJ^WJO', 'I~nKZ]WMG'], ['IbCLJNZZO', 'IbCLHnZZO'], ['Ijv{N^g]?', 'Iv~]NeLM?'], ['Ir`h|VIm?', 'IzLHymHWW'], ['IbPgl~N}O', 'InkzGF^gw'], ['IfaKnMNM?', 'Iz?NjFL]?'], ['IrfhKMGHW', 'IjWHrNci?'], ['IrtxlNJGW', 'IzTw\\eNWW'], ['I~\\Y|]HiW', 'Izmmmemko'], ['Izh^GMjXw', 'Izh]GNjXw'], ['IrDZMF|~o', 'Id{gx^Vzg'], ['IjFyNMhiW', 'IjFyNMjIW'], ['IbVgNeiho', 'IrCz[UxXG'], ['IvXz\\Epgw', 'InXz\\Epgw'], ['IrSI{cVUG', 'IrSG{sVUG'], ['IbYjxEig?', 'IzOnhEYI?'], ['Ib?yjeKiw', 'IrDYh]wGW'], ['IbgJLfWi?', 'IfCi|EGhO'], ['IbSiH}]y?', 'IrFjg]GwW'], ['IjvmleZn_', 'Iv^ilM]mW'], ['IbjxnfIi_', 'IrwyWnJXW'], ['IbjxnfIi_', 'IvWY~MshG'], ['Ib`WjEJiO', 'IjoGhMihO'], ['IbM}LmGhO', 'IbSZ|f[GG'], ['IbkMHeGwO', 'IbKMXeGwO'], ['IfYghUGio', 'IrdGo}EcW'], ['In]JhUMio', 'IrQ\\|fWmO'], ['Ir\\YlUGmO', 'InAM|]G}?'], ['IjsW~eMzO', 'I~LGYM|Xw'], ['IrTWXEYkW', 'IbOh[NWzO'], ['Iv@i\\eLWG', 'IbPIpMtlO'], ['IfPwJ]gXG', 'Il[zhEKw?'], ['IbxiZUIW?', 'IrE[{cUAg'], ['IbZG|FJ[?', 'IbCNhMk]O'], ['InEkXNYI?', 'Ir`KwdTrG'], ['IzxLLmMN_', 'IfziNmwM_'], ['Iru[{}WG?', 'Ivfl{kS?G'], ['IvWhWMWg?', 'IfwhWMWg?'], ['IbgI{mhj?', 'IbgIwmhn?'], ['IrwyWnJXW', 'IvWY~MshG'], ['IbDHkUxio', 'IbDj[FwMO'], ['InFgIFm{O', 'InFgIEm|O'], ['IfOIzMehG', 'IbWJvMchG'], ['I`K[CAsEG', 'I`k{C?sAG'], ['IbgMxeIm?', 'IfI[[U?}G'], ['IrSJ\\min_', 'Ib@Kn^m}G'], ['IbDgh]mig', 'IbDgju}i?'], ['IrVK~uMm_', 'Ifj]W}ymO'], ['IvXKnmJiG', 'IzDjzM[gW'], ['IbBGjeI~w', 'IzXMJFL]?'], ['InA\\hV[yW', 'InfXZFHN_'], ['Ibykx]GgO', 'Ij[IxEiiO'], ['IfVWlu[lO', 'I~Kj^VgWO'], ['Ijq]hUKgw', 'IzYygVHgW'], ['Ijq]hUKgw', 'IfXW\\e`lg'], ['Ijq]hUKgw', 'IbSlvMehG'], ['IbQ\\lU\\lO', 'Ibdl|Ehn?'], ['IfWH|EMjO', 'IvC[HNKyW'], ['IjWKlEHwW', 'Ib^GHEX[W'], ['IjQHxFYxo', 'IvgmHmNi?'], ['Ibw}|]\\gW', 'Iv]|IMi{o'], ['If}[~U]hW', 'Iv{Z[MX}w'], ['I~BWLvkzG', 'Ij}l^]UGG'], ['Iji[xMG{?', 'IvtISKVCW'], ['I~@yjMJXw', 'I~[NLmGxo'], ['Ir@ghM~wG', 'IjG|\\U{GG'], ['Ij}YlMWYG', 'IbWNtMdn_'], ['IzIIlN[zG', 'IrpZLFyNG'], ['IzIIlN[zG', 'I~cikeJNo'], ['IzIIlN[zG', 'IbTz]Ewjg'], ['IrjYxEI]_', 'If[NW}GlO'], ['IjCMhNKiG', 'IrJILEJMG'], ['Ifd\\HNGzO', 'IjqKJUZmO'], ['Ib`{HNKm?', 'IrSjHNoi?'], ['IrpZLFyNG', 'I~cikeJNo'], ['IrpZLFyNG', 'IbTz]Ewjg'], ['IziMN^nM?', 'IjyMN^nM?'], ['Ibu[^~XM?', 'Ivm[xvGMo'], ['IvdkNmGm?', 'Irs[gFG^w'], ['I~JXHN\\G?', 'IvC^sfl?G'], ['Ir\\kgFGYw', 'Irt{wEGWw'], ['IzYygVHgW', 'IfXW\\e`lg'], ['IzYygVHgW', 'IbSlvMehG'], ['IvCmLugYW', 'IbXGpmnio'], ['I~cikeJNo', 'IbTz]Ewjg'], ['IjCi|uHMW', 'IbDi{}HMW'], ['IjC}kuMxw', 'I~EmYEZ{W'], ['IfViINNzW', 'I~RxrNshG'], ['Iff]wEU^G', 'Ifv]wEQ^G'], ['IfXW\\e`lg', 'IbSlvMehG'], ['InO\\^FNGG', 'InOX^NNGG'], ['IrT{pMFg?', 'IrPmpmMg?'], ['IrUk|Ugi?', 'IzWmhUYI_'], ['Ij`iLnyiG', 'IvyGj]YwO'], ['Ij`iLnyiG', 'IduKhV`^o'], ['IzSn\\mI}_', 'Ijw|JFmhw'], ['Iz@[~uImG', 'Ij^Ghm]yO'], ['Ij@Kh]Iy_', 'Ibo[hE\\kO'], ['IbfKjuMjG', 'IjUgIem}o'], ['Iv]i^EG{O', 'In[mL]GmO'], ['IreIL][gO', 'IrQLlUMgO'], ['IreIL][gO', 'IrEh^EkgG'], ['IvyGj]YwO', 'IduKhV`^o'], ['IrQLlUMgO', 'IrEh^EkgG'], ['Ir{MlFMhO', 'IfpMLeMnG'], ['IbwH|UNhO', 'IjTHNEw}O'], ['IfB[|UGgO', 'I|O{hEkw?'], ['IbUgzvXgO', 'IjFJjEh]_'], ['IrT[JE~go', 'IvOWze]xO'], ['If[LXUXW?', 'IrIzXEG{?'], ['Ir{k|MGy?', 'Ivkk]E?|g'], ['Ibv^NnGZO', 'IzH~^EHhw'], ['IbPM^EgM?', 'IfGMgmJi?'], ['I~~k|vmm?', 'I~nl^m{jO'], ['I~yM^M}n_', 'Izw^zU^hw'], ['Ibe^jfXM?', 'IfzKZUw]?'], ['IbMI\\nIg?', 'IjEh]vGGG'], ['IzkZGN~wW', 'Izzhpncig'], ['IjFl^mwjO', 'IbW{t}||?'], ['IfTNkMwYo', 'IzDikFNJW'], ['InnHKemJo', 'IzDiLfZjO'], ['IzSgMMiwW', 'IrSgNMiwW'], ['I|El\\^?G?', 'Iv?N[ff?G'], ['IzZ~[tt?G', 'IzZ^]tt?G'], ['I~Il~EGg?', 'Ib{MxEI]_'], ['IzsLjUIi?', 'IzlGUtfAG'], ['Irol~MYxw', 'IbHY|]m~o'], ['IbOjHnY~w', 'Iz|k[uJYO'], ['IvXGn~}}_', 'InZMhm}yw'], ['IrDGh~Jm_', 'IvYINEyN?'], ['InHGjnijG', 'InHGjminG'], ['Ijc[HVGko', 'IbSMHmYgW'], ['IjoGhEhgo', 'IboipMFg?'], ['IfT]~EljO', 'Ibw]rMvz_'], ['IbWGhNZlO', 'IbtLKegJo'], ['IrhyxUGgO', 'IjOkLNGz_'], ['IbRG\\vWhO', 'IfRhZEwWO'], ['IzOKLM\\lw', 'IjxWHfmyO'], ['If_HxUJwG', 'IfgHxUHwG'], ['Ij@}NnK[?', 'Ih[NpeMy_'], ['Irk\\HngYG', 'Ivc\\LnGYG'], ['IrDKXNIMG', 'IbakjNHM?'], ['IrPM\\Eh}_', 'IfsJhFbZ_'], ['If`]\\ekM?', 'Ibd]\\ekM?'], ['IjhGNUJNO', 'Ij`GNUJnO'], ['Ij\\klv}m?', 'IzXklv}m?'], ['Ib@[LuzN?', 'IbkMKmwiW'], ['Ib@[LuzN?', 'IrNHKMwiW'], ['IbqXJMHmo', 'IvZ[RM@Gw'], ['IbkMKmwiW', 'IrNHKMwiW'], ['I~XnjmGjO', 'InxyznMg?'], ['I~W\\I^WXw', 'Ibvhyejko'], ['IrlwwEGIw', 'IzLlgV?go'], ['IvDWwE]lW', 'If{]]U?]G'], ['IzLIi}MyW', 'Ijvhke|Ho'], ['IzgzHN~WW', 'IzNxLM{jO'], ['Ib^mJeigo', 'Iz@y[U\\Ww'], ['IrUiYUmgo', 'IbMiYUmwo'], ['InoL~eGi?', 'Ij@hjN[Wg'], ['IbWNzFKi_', 'IjRiHNwwO'], ['Ib}MzUIi?', 'IrHNxUii_'], ['Ibc}\\mIyo', 'IfqWjnI\\W'], ['IbpiJmYm?', 'IjUIlFMhO'], ['IbpiJmYm?', 'IvTwIMigo'], ['IfDmLuY~?', 'IbW|jUYww'], ['IfDmLuY~?', 'IjO|jUYiw'], ['If?MHmYjw', 'IfALxEyxO'], ['If~ZLUjgW', 'I~EwyMn{O'], ['IrkMHeGwO', 'IbKNXeGwO'], ['IvQX|VGiO', 'IrL^HNgYG'], ['IjUMx]inW', 'IvFLX]Xyw'], ['IjUMx]inW', 'IvgzM]xYW'], ['IjUMx]inW', 'I~Uy{eJjO'], ['IjUIlFMhO', 'IvTwIMigo'], ['IrsG|EXgw', 'IzQXzMMg?'], ['IbyyXFWko', 'IjOl[N[jO'], ['IjOKNN|ko', 'Ifk}WFJio'], ['IbtWH}ZgO', 'IvEx]EkgG'], ['IbW|jUYww', 'IjO|jUYiw'], ['IvPgHEKYG', 'IzFGGEWLW'], ['IvFLX]Xyw', 'IvgzM]xYW'], ['IvFLX]Xyw', 'I~Uy{eJjO'], ['Ib{JxUIY_', 'IzwlXUwI?'], ['IjhMXELW?', 'IjhLXELW?'], ['In`kX^I[?', 'In_kX^i[?'], ['InQI\\Mi[?', 'IjRI\\ehM?'], ['IjTknVnMO', 'Iz^Jj]JgW'], ['IfbGlvI}o', 'IfvGlvI]_'], ['IbRGn^InW', 'IvG]zEXkw'], ['IbQMLuN^?', 'IbQMLe^^?'], ['IfAHnEKMO', 'IbP[{UggG'], ['Ijq]JFZN_', 'IrlX]ehIw'], ['Iba|NmHMo', 'In{m[UgWW'], ['IbPI[]~G?', 'IzlJTsK?G'], ['IrhjY]hG?', 'Iz~KhEeG?'], ['Ij\\jKNYzO', 'IrZzh]HhW'], ['IvGNh}ni?', 'IvGMl}ni?'], ['Iz]^KN^Nw', 'Ir^^VNvMg'], ['IrVylM^~w', 'I~ty~fT\\W'], ['IvgzM]xYW', 'I~Uy{eJjO'], ['Izl~GMxWW', 'IdvjlNDZO'], ['IzLL]FyIO', 'If|n[EgXO'], ['I~Dw{eM[W', 'IzF{K]M[W'], ['IfvxMnj|o', 'Izu^rNvHw'], ['Ifehj]~lo', 'I~}WVM\\Lw'], ['It\\gxN^~?', 'IrRIr}nyg'], ['IvDHuEn?G', 'IzSXUEv?G']]
##### EDGES (evidence of no example on <=10 vertices) ####### 
       
### Finds cospectral graphs with different size, no results on 5 for x in L5: unique_list = [] size=[] for y in x: size.append(Graph(y).size()) for y in size: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different size, no results on 6 for x in L6: unique_list = [] size=[] for y in x: size.append(Graph(y).size()) for y in size: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different size, no results on 7 for x in L7: unique_list = [] size=[] for y in x: size.append(Graph(y).size()) for y in size: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different size, no results on 8 for x in L8: unique_list = [] size=[] for y in x: size.append(Graph(y).size()) for y in size: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different size, no results on 9 for x in L9: unique_list = [] size=[] for y in x: size.append(Graph(y).size()) for y in size: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different size, no results on 10 for x in L10: unique_list = [] size=[] for y in x: size.append(Graph(y).size()) for y in size: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
##### DIAMETER (evidence of no example on <=10 vertices) ####### 
       
### Finds cospectral graphs with different diameter, no results on 5 for x in L5: unique_list = [] diam=[] for y in x: diam.append(Graph(y).diameter()) for y in diam: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different diameter, no results on 6 for x in L6: unique_list = [] diam=[] for y in x: diam.append(Graph(y).diameter()) for y in diam: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different diameter, no results on 7 for x in L7: unique_list = [] diam=[] for y in x: diam.append(Graph(y).diameter()) for y in diam: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different diameter, no results on 8 for x in L8: unique_list = [] diam=[] for y in x: diam.append(Graph(y).diameter()) for y in diam: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different diameter, no results on 9 for x in L9: unique_list = [] diam=[] for y in x: diam.append(Graph(y).diameter()) for y in diam: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
### Finds cospectral graphs with different diameter, no results on 10 for x in L10: unique_list = [] diam=[] for y in x: diam.append(Graph(y).diameter()) for y in diam: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x 
       
##### GIRTH (evidence of no example on <=10 vertices) ####### 
       
### Finds cospectral graphs with different girth, no results on 5 for x in L5: unique_list = [] girths=[] for y in x: girths.append(Graph(y).girth()) for y in girths: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with different girth, no results on 6 for x in L6: unique_list = [] girths=[] for y in x: girths.append(Graph(y).girth()) for y in girths: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with different girth, no results on 7 for x in L7: unique_list = [] girths=[] for y in x: girths.append(Graph(y).girth()) for y in girths: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with different girth, no results on 8 for x in L8: unique_list = [] girths=[] for y in x: girths.append(Graph(y).girth()) for y in girths: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with different girth, no results on 9 for x in L9: unique_list = [] girths=[] for y in x: girths.append(Graph(y).girth()) for y in girths: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with different girth, no results on 10 for x in L10: unique_list = [] girths=[] for y in x: girths.append(Graph(y).girth()) for y in girths: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
##### DEGREE SEQUENCE, TRANSMISSION SEQUENCE, AND NUMBER OF CONNECTED COMPONENTS OF THE COMPLEMENT ####### 
       
### Finds cospectral graphs with a different number of complement connected component for x in L5: unique_list = [] components=[] for y in x: Gbar=Graph(y).complement() components.append(Gbar.connected_components_number()) for y in components: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
['D|g', 'Dxw']
[3, 2]
['D|g', 'Dxw']
[3, 2]
### Finds cospectral graphs with different degree sequences for x in L5: unique_list=[] degseq=[] for y in x: degseq.append(Graph(y).degree_sequence()) for y in degseq: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
['D|g', 'Dxw']
[[4, 4, 2, 2, 2], [4, 3, 3, 3, 1]]
['D|g', 'Dxw']
[[4, 4, 2, 2, 2], [4, 3, 3, 3, 1]]
### Finds cospectral graphs with different transmission sequences for x in L5: unique_list=[] transseq=[] for y in x: transseq.append(trs(Graph(y))) for y in transseq: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
['D|g', 'Dxw']
[[4, 4, 6, 6, 6], [4, 5, 5, 5, 7]]
['D|g', 'Dxw']
[[4, 4, 6, 6, 6], [4, 5, 5, 5, 7]]
A1=Graph('D|g') A2=Graph('Dxw') 
       
A1 
       
A2 
       
A1.complement() 
       
A2.complement() 
       
A1.degree_sequence() 
       
[4, 4, 2, 2, 2]
[4, 4, 2, 2, 2]
A2.degree_sequence() 
       
[4, 3, 3, 3, 1]
[4, 3, 3, 3, 1]
trs(A1) 
       
[4, 4, 6, 6, 6]
[4, 4, 6, 6, 6]
trs(A2) 
       
[4, 5, 5, 5, 7]
[4, 5, 5, 5, 7]
### Checks the graphs are cospectral SignDistLapla(A1).charpoly()-SignDistLapla(A2).charpoly() 
       
0
0
SignDistLapla(A1).charpoly() 
       
x^5 - 26*x^4 + 249*x^3 - 1132*x^2 + 2480*x - 2112
x^5 - 26*x^4 + 249*x^3 - 1132*x^2 + 2480*x - 2112
#### PLANARITY ##### 
       
### Finds cospectral graphs with where one is planar and one is not for x in L5: unique_list = [] planar=[] for y in x: planar.append(Graph(y).is_planar()) for y in planar: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with where one is planar and one is not for x in L6: unique_list = [] planar=[] for y in x: planar.append(Graph(y).is_planar()) for y in planar: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with where one is planar and one is not for x in L7: unique_list = [] planar=[] for y in x: planar.append(Graph(y).is_planar()) for y in planar: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
### Finds cospectral graphs with where one is planar and one is not for x in L8: unique_list = [] planar=[] for y in x: planar.append(Graph(y).is_planar()) for y in planar: if y not in unique_list: unique_list.append(y) if len(unique_list)>1: print x print unique_list 
       
['GnalP?', 'GjqlP?']
[True, False]
['GlQl@?', 'GhQlP?']
[True, False]
['GpN^H?', 'GxNMX?']
[True, False]
['GhxLH?', 'Gxsm@?']
[False, True]
['GnalP?', 'GjqlP?']
[True, False]
['GlQl@?', 'GhQlP?']
[True, False]
['GpN^H?', 'GxNMX?']
[True, False]
['GhxLH?', 'Gxsm@?']
[False, True]
B1=Graph('GpN^H?') B2=Graph('GxNMX?') 
       
B1 
       
B2 
       
B1.is_planar() 
       
True
True
B2.is_planar() 
       
False
False
### Checks the graphs are cospectral SignDistLapla(B1).charpoly()-SignDistLapla(B2).charpoly() 
       
0
0
SignDistLapla(B1).charpoly() 
       
x^8 - 88*x^7 + 3296*x^6 - 69002*x^5 + 886299*x^4 - 7169822*x^3 +
35735188*x^2 - 100453184*x + 122045040
x^8 - 88*x^7 + 3296*x^6 - 69002*x^5 + 886299*x^4 - 7169822*x^3 + 35735188*x^2 - 100453184*x + 122045040