Values
([],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
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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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