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Journal of Applied Mathematics and Computing

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17-11-2021 | Original Research

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

Published in: Journal of Applied Mathematics and Computing | Issue 5/2022

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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 \(\sigma ({\mathcal {H}})\) of the corresponding double hexagonal (benzenoid) chain \({\mathcal {H}}\). As the result, we compute \(\sigma ({\mathcal {H}})\) of \({\mathcal {H}}\) by means of a product of some of obtained six matrices and a vector with entries in \({\mathbb {N}}\). 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.

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Title: Computing the Merrifield-Simmons indices of benzenoid chains and double benzenoid chains
Publication date: 17-11-2021
Published in: Journal of Applied Mathematics and Computing / Issue 5/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01659-x

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