The Merrifield-Simmons index for two types of phenylenes

Abstract

The Merrifield-Simmons index i(G) of a simple undirected graph G=(V,E) is the number of all independent sets of vertices in G. This number is one of the most popular topological indices in chemistry. In this contribution we obtain exact formulas for the Merrifield-Simmons index of two types of the branched phenylenes whose molecular graph consists of two linear chains of alternating hexagons and quadrangles, together forming a bent chain.