Identifier
Identifier
Values
([],0) generating graphics... => 1
([],1) generating graphics... => 1
([],2) generating graphics... => 1
([(0,1)],2) generating graphics... => 1
([],3) generating graphics... => 1
([(1,2)],3) generating graphics... => 3
([(0,2),(1,2)],3) generating graphics... => 3
([(0,1),(0,2),(1,2)],3) generating graphics... => 1
([],4) generating graphics... => 1
([(2,3)],4) generating graphics... => 5
([(1,3),(2,3)],4) generating graphics... => 8
([(1,2),(1,3),(2,3)],4) generating graphics... => 2
([(0,3),(1,3),(2,3)],4) generating graphics... => 2
([(0,3),(1,2)],4) generating graphics... => 2
([(0,3),(1,2),(2,3)],4) generating graphics... => 6
([(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 4
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 0
([],5) generating graphics... => 1
([(3,4)],5) generating graphics... => 9
([(2,4),(3,4)],5) generating graphics... => 24
([(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(1,4),(2,4),(3,4)],5) generating graphics... => 14
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 3
([(1,4),(2,3)],5) generating graphics... => 12
([(1,4),(2,3),(3,4)],5) generating graphics... => 42
([(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 36
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 9
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 15
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 2
([(0,1),(2,4),(3,4)],5) generating graphics... => 21
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 36
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 15
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 36
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 30
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 30
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 24
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 6
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 24
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 18
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) generating graphics... => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 0
([(0,1),(2,3),(2,4),(3,4)],5) generating graphics... => 6
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 30
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 24
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 6
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 6
([],6) generating graphics... => 1
([(4,5)],6) generating graphics... => 11
([(3,5),(4,5)],6) generating graphics... => 33
([(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(2,5),(3,5),(4,5)],6) generating graphics... => 26
([(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 2
([(2,5),(3,4)],6) generating graphics... => 22
([(2,5),(3,4),(4,5)],6) generating graphics... => 68
([(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 52
([(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(1,2),(3,5),(4,5)],6) generating graphics... => 59
([(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 98
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 41
([(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 82
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 68
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 62
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 52
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 7
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 10
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 36
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 26
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 11
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,2),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 54
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 40
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,1),(2,5),(3,5),(4,5)],6) generating graphics... => 14
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 26
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,5),(1,5),(2,4),(3,4)],6) generating graphics... => 17
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 16
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 52
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 50
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 18
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 10
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 23
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 22
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) generating graphics... => 5
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 14
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 16
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 28
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 28
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) generating graphics... => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) generating graphics... => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,5),(1,4),(2,3)],6) generating graphics... => 4
([(0,1),(2,5),(3,4),(4,5)],6) generating graphics... => 32
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 36
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 8
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) generating graphics... => 20
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 12
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 14
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 48
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) generating graphics... => 36
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 52
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 8
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 32
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 48
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 24
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 44
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 6
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) generating graphics... => 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 0
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 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) generating graphics... => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) generating graphics... => 0
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 4
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 2
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 0
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 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) generating graphics... => 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) generating graphics... => 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) generating graphics... => 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) generating graphics... => 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) generating graphics... => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 0
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 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) generating graphics... => 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) generating graphics... => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 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) generating graphics... => 0
click to show generating function       
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(False)):
            good += 1
    return good/G.automorphism_group().cardinality()

Created
Apr 27, 2019 at 22:17 by Martin Rubey
Updated
Apr 27, 2019 at 22:17 by Martin Rubey