Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000300
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Mapping
St000300: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 2
([],2)
 => 4
([(0,1)],2)
 => 3
([],3)
 => 8
([(1,2)],3)
 => 6
([(0,2),(1,2)],3)
 => 5
([(0,1),(0,2),(1,2)],3)
 => 4
([],4)
 => 16
([(2,3)],4)
 => 12
([(1,3),(2,3)],4)
 => 10
([(0,3),(1,3),(2,3)],4)
 => 9
([(0,3),(1,2)],4)
 => 9
([(0,3),(1,2),(2,3)],4)
 => 8
([(1,2),(1,3),(2,3)],4)
 => 8
([(0,3),(1,2),(1,3),(2,3)],4)
 => 7
([(0,2),(0,3),(1,2),(1,3)],4)
 => 7
([(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)
 => 5
([],5)
 => 32
([(3,4)],5)
 => 24
([(2,4),(3,4)],5)
 => 20
([(1,4),(2,4),(3,4)],5)
 => 18
([(0,4),(1,4),(2,4),(3,4)],5)
 => 17
([(1,4),(2,3)],5)
 => 18
([(1,4),(2,3),(3,4)],5)
 => 16
([(0,1),(2,4),(3,4)],5)
 => 15
([(2,3),(2,4),(3,4)],5)
 => 16
([(0,4),(1,4),(2,3),(3,4)],5)
 => 14
([(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13
([(1,3),(1,4),(2,3),(2,4)],5)
 => 14
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 12
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 11
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 11
([(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)
 => 13
([(0,1),(2,3),(2,4),(3,4)],5)
 => 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 11
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 10
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 11
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 10
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 10
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 8
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 9
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 8
Description
The number of independent sets of vertices of a graph. An independent set of vertices of a graph $G$ is a subset $U \subset V(G)$ such that no two vertices in $U$ are adjacent. This is also the number of vertex covers of $G$ as the map $U \mapsto V(G)\setminus U$ is a bijection between independent sets of vertices and vertex covers. The size of the largest independent set, also called independence number of $G$, is [[St000093]]