The expected values of the total numbers of independent edge sets and independent sets in random alpha-type pentagonal chains

Abstract

A independent edge set of G containing mutually independent edges is also called a matching of G. The total numbers of matchings and independent sets of a graph G, namely, the Hosoya index and the Merrifield-Simmons index, respectively, are two important topological indices. We compute the average total numbers of independent edge sets and independent sets in random alpha-type pentagonal chains.

Keywords

• Matchings
• Independent sets
• Auxiliary graph
• Alpha-type pentagonal chains