Identifier
Values
0 => ([(0,1)],2) => ([],2) => 1
1 => ([(0,1)],2) => ([],2) => 1
00 => ([(0,2),(2,1)],3) => ([],3) => 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
11 => ([(0,2),(2,1)],3) => ([],3) => 1
000 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 1
111 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
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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 $x=y=2$.
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.