Identifier
Identifier
Values
([],1) generating graphics... => 2
([],2) generating graphics... => 4
([(0,1)],2) generating graphics... => 3
([],3) generating graphics... => 8
([(1,2)],3) generating graphics... => 6
([(0,2),(1,2)],3) generating graphics... => 5
([(0,1),(0,2),(1,2)],3) generating graphics... => 4
([],4) generating graphics... => 16
([(2,3)],4) generating graphics... => 12
([(1,3),(2,3)],4) generating graphics... => 10
([(1,2),(1,3),(2,3)],4) generating graphics... => 8
([(0,3),(1,3),(2,3)],4) generating graphics... => 9
([(0,3),(1,2)],4) generating graphics... => 9
([(0,3),(1,2),(2,3)],4) generating graphics... => 8
([(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 7
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 7
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 6
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 5
([],5) generating graphics... => 32
([(3,4)],5) generating graphics... => 24
([(2,4),(3,4)],5) generating graphics... => 20
([(2,3),(2,4),(3,4)],5) generating graphics... => 16
([(1,4),(2,4),(3,4)],5) generating graphics... => 18
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 17
([(1,4),(2,3)],5) generating graphics... => 18
([(1,4),(2,3),(3,4)],5) generating graphics... => 16
([(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 14
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 14
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 12
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 10
([(0,1),(2,4),(3,4)],5) generating graphics... => 15
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 14
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 13
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 13
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 12
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 12
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 11
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 11
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 10
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 11
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 10
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) generating graphics... => 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 6
([(0,1),(2,3),(2,4),(3,4)],5) generating graphics... => 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 11
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 10
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 9
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 10
([],6) generating graphics... => 64
([(4,5)],6) generating graphics... => 48
([(3,5),(4,5)],6) generating graphics... => 40
([(3,4),(3,5),(4,5)],6) generating graphics... => 32
([(2,5),(3,5),(4,5)],6) generating graphics... => 36
([(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 34
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 33
([(2,5),(3,4)],6) generating graphics... => 36
([(2,5),(3,4),(4,5)],6) generating graphics... => 32
([(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 28
([(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 28
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 24
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(1,2),(3,5),(4,5)],6) generating graphics... => 30
([(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 28
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 26
([(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 26
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 24
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 24
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 22
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 22
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 22
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 18
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 16
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(1,2),(3,4),(3,5),(4,5)],6) generating graphics... => 24
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 22
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 20
([(0,1),(2,5),(3,5),(4,5)],6) generating graphics... => 27
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 26
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 25
([(0,5),(1,5),(2,4),(3,4)],6) generating graphics... => 25
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 24
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 23
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 22
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 21
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 20
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 19
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 19
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 22
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 21
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) generating graphics... => 20
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 19
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 17
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 18
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 17
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 17
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 16
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 15
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 17
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) generating graphics... => 16
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) generating graphics... => 15
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,5),(1,4),(2,3)],6) generating graphics... => 27
([(0,1),(2,5),(3,4),(4,5)],6) generating graphics... => 24
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 21
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 20
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 19
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 21
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 15
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) generating graphics... => 19
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 15
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 15
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 17
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 17
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 16
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 15
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 18
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 22
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 20
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) generating graphics... => 21
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 19
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 17
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 20
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 19
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 18
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 17
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 17
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) generating graphics... => 16
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 15
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 15
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) generating graphics... => 18
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 16
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 14
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 13
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 13
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) generating graphics... => 14
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 15
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 17
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 15
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 14
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) generating graphics... => 15
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 14
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 13
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 13
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 11
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 10
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 16
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 14
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 15
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 12
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
click to show generating function       
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 St000093The length of the maximal independent set of vertices of a graph.
References
Code
def statistic(G):
    return sum( 1 for S in Subsets(G) if G.is_independent_set(S) )
Created
Nov 26, 2015 at 12:23 by Christian Stump
Updated
Oct 28, 2016 at 13:17 by Martin Rubey