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.
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
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