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Identifier
Values
=>
Cc0020;cc-rep
([],0)=>1 ([],1)=>1 ([],2)=>1 ([(0,1)],2)=>1 ([],3)=>1 ([(1,2)],3)=>3 ([(0,2),(1,2)],3)=>3 ([(0,1),(0,2),(1,2)],3)=>1 ([],4)=>1 ([(2,3)],4)=>5 ([(1,3),(2,3)],4)=>8 ([(0,3),(1,3),(2,3)],4)=>2 ([(0,3),(1,2)],4)=>2 ([(0,3),(1,2),(2,3)],4)=>6 ([(1,2),(1,3),(2,3)],4)=>2 ([(0,3),(1,2),(1,3),(2,3)],4)=>4 ([(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)=>0 ([],5)=>1 ([(3,4)],5)=>9 ([(2,4),(3,4)],5)=>24 ([(1,4),(2,4),(3,4)],5)=>14 ([(0,4),(1,4),(2,4),(3,4)],5)=>3 ([(1,4),(2,3)],5)=>12 ([(1,4),(2,3),(3,4)],5)=>42 ([(0,1),(2,4),(3,4)],5)=>21 ([(2,3),(2,4),(3,4)],5)=>7 ([(0,4),(1,4),(2,3),(3,4)],5)=>36 ([(1,4),(2,3),(2,4),(3,4)],5)=>36 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>15 ([(1,3),(1,4),(2,3),(2,4)],5)=>9 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>30 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>15 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>30 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>24 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>4 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,3),(2,3),(2,4)],5)=>36 ([(0,1),(2,3),(2,4),(3,4)],5)=>6 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>30 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>6 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>6 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>24 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>18 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>24 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>9 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>3 ([(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)=>0 ([],6)=>1 ([(4,5)],6)=>11 ([(3,5),(4,5)],6)=>33 ([(2,5),(3,5),(4,5)],6)=>26 ([(1,5),(2,5),(3,5),(4,5)],6)=>11 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(2,5),(3,4)],6)=>22 ([(2,5),(3,4),(4,5)],6)=>68 ([(1,2),(3,5),(4,5)],6)=>59 ([(3,4),(3,5),(4,5)],6)=>8 ([(1,5),(2,5),(3,4),(4,5)],6)=>98 ([(0,1),(2,5),(3,5),(4,5)],6)=>14 ([(2,5),(3,4),(3,5),(4,5)],6)=>52 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>26 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>41 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>12 ([(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,5),(1,5),(2,4),(3,4)],6)=>17 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>62 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>52 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>18 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>68 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>16 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>23 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>52 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>50 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>22 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>7 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>18 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>10 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>18 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(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)=>4 ([(1,5),(2,4),(3,4),(3,5)],6)=>82 ([(0,1),(2,5),(3,4),(4,5)],6)=>32 ([(1,2),(3,4),(3,5),(4,5)],6)=>12 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>48 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>54 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>20 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>36 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>8 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>10 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>32 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>36 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>24 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>40 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>12 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>44 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>48 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>26 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>20 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>36 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>5 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>20 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>16 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>52 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>14 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>6 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>14 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>16 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>13 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>10 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>28 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>8 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>11 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>10 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>2 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>4 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>12 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>8 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>28 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>12 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>6 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4 ([(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)=>2 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(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)=>2 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(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)=>6 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(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)=>0 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(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)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>0 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>6 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>0 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>4 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>0 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(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)=>0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0
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Description
The number of prime labellings of a graph.
A prime labelling of a graph is a bijective labelling of the vertices with the numbers $\{1,\dots, |V(G)|\}$ such that adjacent vertices have coprime labels.
References
[1] Andreson, M. Prime labelling of graphs MathOverflow:191182
Code
def statistic(G):
    G.relabel(inplace=False)
    n = G.num_verts()
    good = 0
    for pi in Permutations(n):
        if all(gcd(pi[u], pi[v]) == 1 for u, v in G.edges(labels=False)):
            good += 1
    return good/G.automorphism_group().cardinality()

Created
Apr 27, 2019 at 22:17 by Martin Rubey
Updated
Dec 23, 2020 at 11:52 by Martin Rubey