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Identifier

St000349: Graphs ⟶ ℤ

Values

([],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) => 6

([(1,3),(2,3)],4) => 12

([(0,3),(1,3),(2,3)],4) => 4

([(0,3),(1,2)],4) => 3

([(0,3),(1,2),(2,3)],4) => 12

([(1,2),(1,3),(2,3)],4) => 4

([(0,3),(1,2),(1,3),(2,3)],4) => 12

([(0,2),(0,3),(1,2),(1,3)],4) => 3

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([],5) => 1

([(3,4)],5) => 10

([(2,4),(3,4)],5) => 30

([(1,4),(2,4),(3,4)],5) => 20

([(0,4),(1,4),(2,4),(3,4)],5) => 5

([(1,4),(2,3)],5) => 15

([(1,4),(2,3),(3,4)],5) => 60

([(0,1),(2,4),(3,4)],5) => 30

([(2,3),(2,4),(3,4)],5) => 10

([(0,4),(1,4),(2,3),(3,4)],5) => 60

([(1,4),(2,3),(2,4),(3,4)],5) => 60

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 30

([(1,3),(1,4),(2,3),(2,4)],5) => 15

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 60

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 30

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 60

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 60

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 10

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10

([(0,4),(1,3),(2,3),(2,4)],5) => 60

([(0,1),(2,3),(2,4),(3,4)],5) => 10

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 60

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 15

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 12

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 60

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 60

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 60

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 20

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 30

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 30

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 15

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10

([(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) => 15

([(3,5),(4,5)],6) => 60

([(2,5),(3,5),(4,5)],6) => 60

([(1,5),(2,5),(3,5),(4,5)],6) => 30

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6

([(2,5),(3,4)],6) => 45

([(2,5),(3,4),(4,5)],6) => 180

([(1,2),(3,5),(4,5)],6) => 180

([(3,4),(3,5),(4,5)],6) => 20

([(1,5),(2,5),(3,4),(4,5)],6) => 360

([(0,1),(2,5),(3,5),(4,5)],6) => 60

([(2,5),(3,4),(3,5),(4,5)],6) => 180

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 120

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 180

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 60

([(2,4),(2,5),(3,4),(3,5)],6) => 45

([(0,5),(1,5),(2,4),(3,4)],6) => 90

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 360

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 360

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 90

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 360

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 90

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 180

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 360

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 360

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 180

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 60

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 180

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 120

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 60

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 180

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 120

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 15

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15

([(0,5),(1,4),(2,3)],6) => 15

([(1,5),(2,4),(3,4),(3,5)],6) => 360

([(0,1),(2,5),(3,4),(4,5)],6) => 180

([(1,2),(3,4),(3,5),(4,5)],6) => 60

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 360

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 360

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 180

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 360

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 90

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 90

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 72

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 360

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 360

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 360

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Description

The number of different adjacency matrices of a graph.
This is the number of different labellings of the graph, or $\frac{|G|!}{|\operatorname{Aut}(G)|}$.

References

[1] mathworld:AdjacencyMatrix
[2] wikipedia:Adjacency_matrix

Code

def statistic(g):
    return factorial(len(g.vertices())) / g.automorphism_group().cardinality()

Created

Dec 26, 2015 at 18:02 by Christian Stump

Updated

Dec 14, 2021 at 11:58 by Martin Rubey