Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000266
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Mapping
St000266: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 1
([(0,1)],2)
 => 1
([],3)
 => 1
([(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 4
([],4)
 => 1
([(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => 1
([(1,2),(1,3),(2,3)],4)
 => 4
([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(0,2),(0,3),(1,2),(1,3)],4)
 => 5
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 14
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 38
([],5)
 => 1
([(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3)],5)
 => 1
([(1,4),(2,3),(3,4)],5)
 => 1
([(0,1),(2,4),(3,4)],5)
 => 1
([(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(1,3),(1,4),(2,3),(2,4)],5)
 => 5
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 5
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 19
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 46
([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 16
([(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)
 => 18
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 48
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 14
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 38
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 38
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 124
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 52
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 134
Description
The number of spanning subgraphs of a graph with the same connected components. A subgraph or factor of a graph is spanning, if it has the same vertex set [1]. The present statistic additionally requires the subgraph to have the same components. It can be obtained by evaluating the Tutte polynomial at the points $x=1$ and $y=2$, see [2,3]. By mistake, [2] refers to this statistic as the number of spanning subgraphs, which would be $2^m$, where $m$ is the number of edges. Equivalently, this would be the evaluation of the Tutte polynomial at $x=y=2$.