IndependentSetCount on LabeledGraph

The sets of vertices, the empty set included, with no two adjacent.

On LabeledGraph

FindStat's St000300. The graph with no vertices has the empty set, so 1.

Called as CombinatorialStat(x, "IndependentSetCount"). The head's page has its examples.

Live

Distribution

Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.

Sizes 1 to

FindStat St000300

The number of independent sets of vertices of a graph.

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.

Object	Value
([],0)	1
([],1)	2
([],2)	4
([],3)	8
([],4)	16
([],5)	32
([],6)	64
([],7)	128

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000300 has the rest.