Computing the Merrifield-Simmons indices of benzenoid chains and double benzenoid chains

Abstract

In this paper, we introduce the Merrifield-Simmons vector defined at a path of corresponding double hexagonal (benzenoid) chain. By utilizing this vector, we present reduction formulae to compute the Merrifield-Simmons index σ(H) of the corresponding double hexagonal (benzenoid) chain H. As the result, we compute σ(H) of H by means of a product of some of obtained six matrices and a vector with entries in N. Subsequently, we introduce the simple Merrifield-Simmons vector defined at an edge of given graph G. By using simple Merrifield-Simmons vector we present reduction formulae to compute the σ(G) where G represents any hexagonal (benzenoid) chain.