On the Number of k-Matchings in Graphs

In this paper, we present exact formulae for p(G, (3), p(G, (4) and p(G, (5) in terms of some degree-based invariants, where G is an undirected simple graph, a k-subset of edges in G without common vertices is called a k-matching and the number of such subsets is denoted by p(G, k). Significance of research work Molecular descriptors play a significant role in mathematical chemistry especially in QSPR/QSAR investigations. Among them, special place is reserved for so-called topological descriptors. Nowadays, there exists a legion of topological indices that found some applications in chemistry. In this paper, we obtain exact formulae for p(G, (3), p(G, (4) and p(G, (5) in terms of some degree-based invariants (topological indices).