## ABSTRACT

Let G be a graph with n vertices. An r-matching in a graph G is a set of r edges, no two of which have a vertex in common. The number of r-matchings in G will be denoted by p(G, r). We set p(G, 0) = 1 and define the matchings polynomial of G by μ ( G , x ) : = ∑ r ≥ 0 ( − 1 ) r p ( G , r ) x n − 2 r . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137131/3e789cab-79f2-434a-a841-e2acf5146c2d/content/eq2.tif"/>