Sum of one over - but not cospectral -- Sage

def make_laplacian(G): L=Matrix(QQ,G.order(),G.order()) for i in range(G.order()): for j in G.neighbors(i): L[i,j]=-1/G.degree(i) L[i,i]=1 return L

def are_cospectral(G,H): A=make_laplacian(G) B=make_laplacian(H) f=A.characteristic_polynomial(x) q=f.coeffs() g=B.characteristic_polynomial(x) r=g.coeffs() return q==r

def one_over_graphs(n,display_graphs=True): x=var('x') print "Working on "+str(n)+" vertex graphs" one_over={} for G in graphs.nauty_geng(str(n)+" -c"): A=make_laplacian(G) #A=G.laplacian_matrix(normalized=True) f=A.characteristic_polynomial(x) q=f.coeffs() t=-1*f[2]/f[1] if t in one_over: one_over[t].append(G.graph6_string()) else: one_over[t]=[G.graph6_string()] if display_graphs: for t in one_over: if len(one_over[t])>1: print "====================================" print "The following graphs have same sum" print "of one over the eigenvalues = "+str(t) for x in one_over[t]: Graph(x).show() print "====================================" print "Qapla!" return one_over

def look_for_subgraphs(n): one_over=one_over_graphs(n,display_graphs=False) for t in one_over: if len(one_over[t])>1: for x in one_over[t]: for y in one_over[t]: if not x==y: G=Graph(x) H=Graph(y) if G.subgraph_search_count(H): if not are_cospectral(G,H): print "Following have same sum of one over = "+str(t) print "And are NOT cospectral" print x,y G.show() H.show() print "===================================="

look_for_subgraphs(4)

Working on 4 vertex graphs
Qapla!

Working on 4 vertex graphs
Qapla!

look_for_subgraphs(5)

Working on 5 vertex graphs
Qapla!
Following have same sum of one over = 7/2
And are NOT cospectral
DT{ D?{

====================================

Working on 5 vertex graphs
Qapla!
Following have same sum of one over = 7/2
And are NOT cospectral
DT{ D?{

====================================

look_for_subgraphs(6)

Working on 6 vertex graphs
Qapla!

Working on 6 vertex graphs
Qapla!

look_for_subgraphs(7)

Working on 7 vertex graphs
Qapla!
Following have same sum of one over = 8
And are NOT cospectral
FCQrW F?bDo

====================================
Following have same sum of one over = 13/2
And are NOT cospectral
F?zVO FCZf?

====================================
Following have same sum of one over = 17/3
And are NOT cospectral
FCqnw F?Bfw

====================================
Following have same sum of one over = 20/3
And are NOT cospectral
FCXno FCQvo

====================================
Following have same sum of one over = 191/35
And are NOT cospectral
FCf~w F?r~w

====================================
Following have same sum of one over = 187/30
And are NOT cospectral
FQjVo FCY^_

====================================
Following have same sum of one over = 38/5
And are NOT cospectral
FQinO FCXmW

====================================

Working on 7 vertex graphs
Qapla!
Following have same sum of one over = 8
And are NOT cospectral
FCQrW F?bDo

====================================
Following have same sum of one over = 13/2
And are NOT cospectral
F?zVO FCZf?

====================================
Following have same sum of one over = 17/3
And are NOT cospectral
FCqnw F?Bfw

====================================
Following have same sum of one over = 20/3
And are NOT cospectral
FCXno FCQvo

====================================
Following have same sum of one over = 191/35
And are NOT cospectral
FCf~w F?r~w

====================================
Following have same sum of one over = 187/30
And are NOT cospectral
FQjVo FCY^_

====================================
Following have same sum of one over = 38/5
And are NOT cospectral
FQinO FCXmW

====================================

html('') look_for_subgraphs(8)

Working on 8 vertex graphs
Qapla!
Following have same sum of one over = 7
And are NOT cospectral
G?`vj{ G??Fvg

====================================
Following have same sum of one over = 9
And are NOT cospectral
G?aJFo G?ABFo

====================================
Following have same sum of one over = 12
And are NOT cospectral
G?ouPw G?b@d_

====================================
Following have same sum of one over = 13/2
And are NOT cospectral
GCe^~w G??F~w

====================================
Following have same sum of one over = 13/2
And are NOT cospectral
GCvUv{ G???F{

====================================
Following have same sum of one over = 21/2
And are NOT cospectral
G?BEDo G?AEDo

====================================
Following have same sum of one over = 29/4
And are NOT cospectral
G?ott{ G?AEL{

====================================
Following have same sum of one over = 29/3
And are NOT cospectral
GCdbMw G?b@bo

====================================
Following have same sum of one over = 29/3
And are NOT cospectral
GCdbMw GCQRUw

====================================
Following have same sum of one over = 39/4
And are NOT cospectral
GCdbF_ GCQRF_

====================================
Following have same sum of one over = 63/8
And are NOT cospectral
GCQbro G?bBRo

====================================
Following have same sum of one over = 73/10
And are NOT cospectral
GCZLlk G?AFb[

====================================
Following have same sum of one over = 65/8
And are NOT cospectral
G?aJfw G?B@fw

====================================
Following have same sum of one over = 69/10
And are NOT cospectral
G?BFfw G??Ffw

====================================
Following have same sum of one over = 69/10
And are NOT cospectral
G?`vnw G??Ffw

====================================
Following have same sum of one over = 69/10
And are NOT cospectral
G?`vnw G?BFfw

====================================
Following have same sum of one over = 95/12
And are NOT cospectral
GCOefw G?`DFw

====================================
Following have same sum of one over = 93/10
And are NOT cospectral
GCdcvg G?r@f_

====================================
Following have same sum of one over = 101/12
And are NOT cospectral
GCQRFk G?ABFs

====================================
Following have same sum of one over = 147/20
And are NOT cospectral
GCXk{{ G?AFK{

====================================
Following have same sum of one over = 129/16
And are NOT cospectral
G?`cv[ G?AEFo

====================================
Following have same sum of one over = 179/24
And are NOT cospectral
GCQfVK G?BDLw

====================================
Following have same sum of one over = 203/30
And are NOT cospectral
G?aN]{ G?BFn[

====================================
Following have same sum of one over = 289/40
And are NOT cospectral
G?aK^w G?BEFw

====================================
Following have same sum of one over = 263/36
And are NOT cospectral
GQil^{ G??Fe[

====================================
Following have same sum of one over = 13
And are NOT cospectral
GCdbE_ G?B@v?

====================================
Following have same sum of one over = 583/84
And are NOT cospectral
GQinvs GCXnvs

====================================
Following have same sum of one over = 20/3
And are NOT cospectral
GQjn^w G?Bvfw

====================================
Following have same sum of one over = 181/20
And are NOT cospectral
GCQTec G?`amK

====================================
Following have same sum of one over = 167/20
And are NOT cospectral
GCQuec G?`vF?

====================================
Following have same sum of one over = 161/20
And are NOT cospectral
G?aK^o G?BENo

====================================
Following have same sum of one over = 197/24
And are NOT cospectral
GCQdbw G?bAV_

====================================
Following have same sum of one over = 281/40
And are NOT cospectral
GCQvl{ G?Bem[

====================================
Following have same sum of one over = 89/10
And are NOT cospectral
GCZUmk G?`fBk

====================================
Following have same sum of one over = 111/14
And are NOT cospectral
GCOed{ G??CFw

====================================
Following have same sum of one over = 463/60
And are NOT cospectral
GCdcv{ G?ABfw

====================================
Following have same sum of one over = 317/44
And are NOT cospectral
GCQu^W G?BDlw

====================================
Following have same sum of one over = 449/48
And are NOT cospectral
GCQrRW G?ABeS

====================================
Following have same sum of one over = 137/12
And are NOT cospectral
GCQRVS G?B@tc

====================================
Following have same sum of one over = 439/60
And are NOT cospectral
GCdffk G?AENs

====================================

Working on 8 vertex graphs
Qapla!
Following have same sum of one over = 7
And are NOT cospectral
G?`vj{ G??Fvg

====================================
Following have same sum of one over = 9
And are NOT cospectral
G?aJFo G?ABFo

====================================
Following have same sum of one over = 12
And are NOT cospectral
G?ouPw G?b@d_

====================================
Following have same sum of one over = 13/2
And are NOT cospectral
GCe^~w G??F~w

====================================
Following have same sum of one over = 13/2
And are NOT cospectral
GCvUv{ G???F{

====================================
Following have same sum of one over = 21/2
And are NOT cospectral
G?BEDo G?AEDo

====================================
Following have same sum of one over = 29/4
And are NOT cospectral
G?ott{ G?AEL{

====================================
Following have same sum of one over = 29/3
And are NOT cospectral
GCdbMw G?b@bo

====================================
Following have same sum of one over = 29/3
And are NOT cospectral
GCdbMw GCQRUw

====================================
Following have same sum of one over = 39/4
And are NOT cospectral
GCdbF_ GCQRF_

====================================
Following have same sum of one over = 63/8
And are NOT cospectral
GCQbro G?bBRo

====================================
Following have same sum of one over = 73/10
And are NOT cospectral
GCZLlk G?AFb[

====================================
Following have same sum of one over = 65/8
And are NOT cospectral
G?aJfw G?B@fw

====================================
Following have same sum of one over = 69/10
And are NOT cospectral
G?BFfw G??Ffw

====================================
Following have same sum of one over = 69/10
And are NOT cospectral
G?`vnw G??Ffw

====================================
Following have same sum of one over = 69/10
And are NOT cospectral
G?`vnw G?BFfw

====================================
Following have same sum of one over = 95/12
And are NOT cospectral
GCOefw G?`DFw

====================================
Following have same sum of one over = 93/10
And are NOT cospectral
GCdcvg G?r@f_

====================================
Following have same sum of one over = 101/12
And are NOT cospectral
GCQRFk G?ABFs

====================================
Following have same sum of one over = 147/20
And are NOT cospectral
GCXk{{ G?AFK{

====================================
Following have same sum of one over = 129/16
And are NOT cospectral
G?`cv[ G?AEFo

====================================
Following have same sum of one over = 179/24
And are NOT cospectral
GCQfVK G?BDLw

====================================
Following have same sum of one over = 203/30
And are NOT cospectral
G?aN]{ G?BFn[

====================================
Following have same sum of one over = 289/40
And are NOT cospectral
G?aK^w G?BEFw

====================================
Following have same sum of one over = 263/36
And are NOT cospectral
GQil^{ G??Fe[

====================================
Following have same sum of one over = 13
And are NOT cospectral
GCdbE_ G?B@v?

====================================
Following have same sum of one over = 583/84
And are NOT cospectral
GQinvs GCXnvs

====================================
Following have same sum of one over = 20/3
And are NOT cospectral
GQjn^w G?Bvfw

====================================
Following have same sum of one over = 181/20
And are NOT cospectral
GCQTec G?`amK

====================================
Following have same sum of one over = 167/20
And are NOT cospectral
GCQuec G?`vF?

====================================
Following have same sum of one over = 161/20
And are NOT cospectral
G?aK^o G?BENo

====================================
Following have same sum of one over = 197/24
And are NOT cospectral
GCQdbw G?bAV_

====================================
Following have same sum of one over = 281/40
And are NOT cospectral
GCQvl{ G?Bem[

====================================
Following have same sum of one over = 89/10
And are NOT cospectral
GCZUmk G?`fBk

====================================
Following have same sum of one over = 111/14
And are NOT cospectral
GCOed{ G??CFw

====================================
Following have same sum of one over = 463/60
And are NOT cospectral
GCdcv{ G?ABfw

====================================
Following have same sum of one over = 317/44
And are NOT cospectral
GCQu^W G?BDlw

====================================
Following have same sum of one over = 449/48
And are NOT cospectral
GCQrRW G?ABeS

====================================
Following have same sum of one over = 137/12
And are NOT cospectral
GCQRVS G?B@tc

====================================
Following have same sum of one over = 439/60
And are NOT cospectral
GCdffk G?AENs

====================================

Sum of one over - but not cospectral

3983 days ago by butler