PerfectMatchingCount on LabeledGraph

The sets of edges that meet every vertex exactly once.

On LabeledGraph

FindStat's St000274. The graph with no vertices has the empty set, so 1.

Called as CombinatorialStat(x, "PerfectMatchingCount"). 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 St000274

The number of perfect matchings of a graph.

The number of perfect matchings of a graph. A matching of a graph $G$ is a subset $F \subset E(G)$ such that no two edges in $F$ share a vertex in common. A perfect matching $F'$ is then a matching such that every vertex in $V(G)$ is incident with exactly one edge in $F'$.

Object	Value
([],1)	0
([],2)	0
([],3)	0
([],4)	0
([],5)	0
([],6)	0
([(0,1)],2)	1
([(1,2)],3)	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000274 has the rest.