- FindStat

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000270
(load all 2 compositions to match this statistic)

St000270: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 1
([],2)
 => 1
([(0,1)],2)
 => 2
([],3)
 => 1
([(1,2)],3)
 => 2
([(0,2),(1,2)],3)
 => 4
([(0,1),(0,2),(1,2)],3)
 => 7
([],4)
 => 1
([(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => 4
([(0,3),(1,3),(2,3)],4)
 => 8
([(0,3),(1,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => 8
([(1,2),(1,3),(2,3)],4)
 => 7
([(0,3),(1,2),(1,3),(2,3)],4)
 => 14
([(0,2),(0,3),(1,2),(1,3)],4)
 => 15
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 24
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 38
([],5)
 => 1
([(3,4)],5)
 => 2
([(2,4),(3,4)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => 8
([(0,4),(1,4),(2,4),(3,4)],5)
 => 16
([(1,4),(2,3)],5)
 => 4
([(1,4),(2,3),(3,4)],5)
 => 8
([(0,1),(2,4),(3,4)],5)
 => 8
([(2,3),(2,4),(3,4)],5)
 => 7
([(0,4),(1,4),(2,3),(3,4)],5)
 => 16
([(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 28
([(1,3),(1,4),(2,3),(2,4)],5)
 => 15
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 30
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 24
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 28
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 48
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 54
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 81
([(0,4),(1,3),(2,3),(2,4)],5)
 => 16
([(0,1),(2,3),(2,4),(3,4)],5)
 => 14
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 28
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 49
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 31
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 52
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 82
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 48
([(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)
 => 76
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 128
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 86
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 134

Description

The number of forests contained in a graph. That is, for a graph

$G = (V,E)$ with vertices

$V$ and edges

$E$ , the number of subsets

$E' \subseteq E$ for which the subgraph

$(V,E')$ is acyclic. If

$T_G(x,y)$ is the Tutte polynomial [2] of

$G$ , then the number of forests contained in

$G$ is given by

$T_G(2,1)$ .