Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001783
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Mapping
St001783: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 1
([],3)
 => 0
([(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => 0
([(0,1),(0,2),(1,2)],3)
 => 3
([],4)
 => 0
([(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => 0
([(0,3),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => 1
([(1,2),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 12
([],5)
 => 0
([(3,4)],5)
 => 6
([(2,4),(3,4)],5)
 => 0
([(1,4),(2,4),(3,4)],5)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => 0
([(1,4),(2,3)],5)
 => 4
([(1,4),(2,3),(3,4)],5)
 => 1
([(0,1),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,3),(3,4)],5)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => 6
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 5
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0
Description
The number of odd automorphisms of a graph. Let $D$ be an arbitrary orientation of a graph $G$. Then an automorphism of $G$ is odd, if it reverses the orientation of an odd number of edges of $D$. The graphs on $n$ vertices without any odd automorphisms are equinumerous with the number of non-isomorphic $n$-team tournaments, see [2]. The odd automorphisms of the complete graphs are precisely the even permutations.