The Merrifield-Simmons index for the linear octagonal chains

Abstract

The Merrifield-Simmons index for a simple undirected graph G=(V,E) is given by the number of subsets U of V such that no two vertices in U are adjacent. This number is one of the most popular topological index in chemistry, which was firstly defined and called as the Fibonacci number of a graph. Octagonal chains are cata-condensed systems of octagons and represent a class of polycyclic conjugated hydrocarbons. In this contribution we obtain an exact formula for the Merrifield-Simmons index of linear octagonal chains.