load("https://raw.githubusercontent.com/jephianlin/minrank_aux/master/load_all.py")
load_all()
xrange test passed Loading Zq_c.pyx... Compiling /home/sageuser/2/.sage/temp/sage.math.iastate.edu/776/tmp_Yk16Iu.pyx... Loading Zq.py... Loading zero_forcing_64.pyx... Compiling /home/sageuser/2/.sage/temp/sage.math.iastate.edu/776/tmp_wHLyVx.pyx... Loading zero_forcing_wavefront.pyx... Compiling /home/sageuser/2/.sage/temp/sage.math.iastate.edu/776/tmp_7MUkKt.pyx... Loading minrank.py... Loading inertia.py... Loading general_Lib.sage... ---sshow, multi_sshow, tuple_generator, minimal_graphs, empty_array, all_one_matrix, elementary_matrix, eigens_multi, sort_dictionary, has_minor, etc. Loading oc_diag_analysis.sage... ---gZ_leq, find_gZ, find_EZ, diagonal_analysis, etc. Loading xi_dict.py... ---SAPreduced_matrix, has_SAP, find_ZFloor, Zsap, etc. Loading mu_dict.py... ---get_mu_from_dict, find_mu, etc. Loading SXP.sage... This code contains extra copy of Z_game, Zell_game, Zplus_game, for the completeness of Zsap_game program. Loading matrix_forcing.py... xrange test passed Loading Zq_c.pyx... Compiling /home/sageuser/2/.sage/temp/sage.math.iastate.edu/776/tmp_Yk16Iu.pyx... Loading Zq.py... Loading zero_forcing_64.pyx... Compiling /home/sageuser/2/.sage/temp/sage.math.iastate.edu/776/tmp_wHLyVx.pyx... Loading zero_forcing_wavefront.pyx... Compiling /home/sageuser/2/.sage/temp/sage.math.iastate.edu/776/tmp_7MUkKt.pyx... Loading minrank.py... Loading inertia.py... Loading general_Lib.sage... ---sshow, multi_sshow, tuple_generator, minimal_graphs, empty_array, all_one_matrix, elementary_matrix, eigens_multi, sort_dictionary, has_minor, etc. Loading oc_diag_analysis.sage... ---gZ_leq, find_gZ, find_EZ, diagonal_analysis, etc. Loading xi_dict.py... ---SAPreduced_matrix, has_SAP, find_ZFloor, Zsap, etc. Loading mu_dict.py... ---get_mu_from_dict, find_mu, etc. Loading SXP.sage... This code contains extra copy of Z_game, Zell_game, Zplus_game, for the completeness of Zsap_game program. Loading matrix_forcing.py... |
def cospectral(n, mtx='adj'):
data = {}
for g in graphs.nauty_geng('%s'%n):
stg = g.canonical_label().graph6_string()
if mtx == 'adj':
A = g.adjacency_matrix()
elif mtx == 'lap':
A = g.laplacian_matrix()
elif mtx == 'dis':
A = g.distance_matrix()
a = A.charpoly().coefficients(sparse=False)
a.reverse()
tup_a = tuple(a)
try:
data[tup_a].append(stg)
except KeyError:
data[tup_a] = [stg]
#return data
return {k:data[k] for k in data.keys() if len(data[k])>=2}
|
|
want = {}
for n in range(1,8):
want[n] = cospectral(n)
|
|
for n in range(1,7):
data = want[n]
for c in data.keys():
gs = data[c]
zs = [find_Z(Graph(stg)) for stg in gs]
if len(set(zs)) >= 2:
print(n,c)
(6, (1, 0, -7, -4, 7, 4, -1)) (6, (1, 0, -6, -4, 5, 4, 0)) (6, (1, 0, -5, 0, 4, 0, 0)) (6, (1, 0, -4, 0, 3, 0, 0)) (6, (1, 0, -7, -4, 7, 4, -1)) (6, (1, 0, -6, -4, 5, 4, 0)) (6, (1, 0, -5, 0, 4, 0, 0)) (6, (1, 0, -4, 0, 3, 0, 0)) |
gs = want[6][(1, 0, -7, -4, 7, 4, -1)]
for stg in gs:
g = Graph(stg)
A = g.adjacency_matrix()
print(A.charpoly())
sshow(g, "Z = %s"%find_Z(g))
x^6 - 7*x^4 - 4*x^3 + 7*x^2 + 4*x - 1 x^6 - 7*x^4 - 4*x^3 + 7*x^2 + 4*x - 1 x^6 - 7*x^4 - 4*x^3 + 7*x^2 + 4*x - 1 x^6 - 7*x^4 - 4*x^3 + 7*x^2 + 4*x - 1  
|
gs = want[6][(1, 0, -6, -4, 5, 4, 0)]
for stg in gs:
g = Graph(stg)
A = g.adjacency_matrix()
print(A.charpoly())
sshow(g, "Z = %s"%find_Z(g))
x^6 - 6*x^4 - 4*x^3 + 5*x^2 + 4*x x^6 - 6*x^4 - 4*x^3 + 5*x^2 + 4*x x^6 - 6*x^4 - 4*x^3 + 5*x^2 + 4*x x^6 - 6*x^4 - 4*x^3 + 5*x^2 + 4*x  
|
gs = want[6][(1, 0, -5, 0, 4, 0, 0)]
for stg in gs:
g = Graph(stg)
A = g.adjacency_matrix()
print(A.charpoly())
sshow(g, "Z = %s"%find_Z(g))
x^6 - 5*x^4 + 4*x^2 x^6 - 5*x^4 + 4*x^2 x^6 - 5*x^4 + 4*x^2 x^6 - 5*x^4 + 4*x^2  
|
gs = want[6][(1, 0, -4, 0, 3, 0, 0)]
for stg in gs:
g = Graph(stg)
A = g.adjacency_matrix()
print(A.charpoly())
sshow(g, "Z = %s"%find_Z(g))
x^6 - 4*x^4 + 3*x^2 x^6 - 4*x^4 + 3*x^2 x^6 - 4*x^4 + 3*x^2 x^6 - 4*x^4 + 3*x^2  
|
|
|
|
|