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


Oz M. S. , CANGÜL İ. N.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1007/s12190-021-01659-x
  • Title of Journal : JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • Keywords: Double benzenoid chains, Double hexagonal chains, Hexagonal chains, Topological index, Merrifield-Simmons index, DOUBLE HEXAGONAL CHAINS, SENSITIVE GRAPHICAL SUBSETS, HOSOYA INDEX, ENUMERATION, RESPECT

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 sigma(H) of the corresponding double hexagonal (benzenoid) chain H. As the result, we compute sigma(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 sigma(G) where G represents any hexagonal (benzenoid) chain.