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Identifier
Values
=>
Cc0020;cc-rep
([],1)=>1 ([],2)=>1 ([(0,1)],2)=>1 ([],3)=>1 ([(1,2)],3)=>1 ([(0,2),(1,2)],3)=>1 ([(0,1),(0,2),(1,2)],3)=>1 ([],4)=>1 ([(2,3)],4)=>1 ([(1,3),(2,3)],4)=>1 ([(0,3),(1,3),(2,3)],4)=>1 ([(0,3),(1,2)],4)=>1 ([(0,3),(1,2),(2,3)],4)=>1 ([(1,2),(1,3),(2,3)],4)=>1 ([(0,3),(1,2),(1,3),(2,3)],4)=>1 ([(0,2),(0,3),(1,2),(1,3)],4)=>1 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>1 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>1 ([],5)=>1 ([(3,4)],5)=>1 ([(2,4),(3,4)],5)=>1 ([(1,4),(2,4),(3,4)],5)=>1 ([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(1,4),(2,3)],5)=>1 ([(1,4),(2,3),(3,4)],5)=>1 ([(0,1),(2,4),(3,4)],5)=>1 ([(2,3),(2,4),(3,4)],5)=>1 ([(0,4),(1,4),(2,3),(3,4)],5)=>1 ([(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(1,3),(1,4),(2,3),(2,4)],5)=>2 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>1 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>1 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>1 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,4),(1,3),(2,3),(2,4)],5)=>1 ([(0,1),(2,3),(2,4),(3,4)],5)=>1 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>1 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>1 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>1 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>1 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>1 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>1 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>1 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([],6)=>1 ([(4,5)],6)=>1 ([(3,5),(4,5)],6)=>1 ([(2,5),(3,5),(4,5)],6)=>1 ([(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>1 ([(2,5),(3,4)],6)=>1 ([(2,5),(3,4),(4,5)],6)=>1 ([(1,2),(3,5),(4,5)],6)=>1 ([(3,4),(3,5),(4,5)],6)=>1 ([(1,5),(2,5),(3,4),(4,5)],6)=>1 ([(0,1),(2,5),(3,5),(4,5)],6)=>2 ([(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>1 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,5),(1,5),(2,4),(3,4)],6)=>1 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3)],6)=>1 ([(1,5),(2,4),(3,4),(3,5)],6)=>2 ([(0,1),(2,5),(3,4),(4,5)],6)=>1 ([(1,2),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>1 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>2 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>2 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>1 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>1 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>1 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>1 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>1 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>1 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>1 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>1 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>1 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>1 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>1 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
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Description
The number of graphs with the same ordinary spectrum as the given graph.
Code
@cached_function
def spectra(n):
    return {G.canonical_label().copy(immutable=True): sorted(G.adjacency_matrix().eigenvalues()) for G in graphs(n)}

def statistic(G):
    d = spectra(G.num_verts())
    s = d[G.canonical_label().copy(immutable=True)]
    return sum(1 for _, s_H in d.items() if s == s_H)
Created
Feb 14, 2020 at 16:27 by Martin Rubey
Updated
Oct 26, 2021 at 16:13 by Martin Rubey