The comparative analysis of two molecular indices in random polyphenyl and spiro chains

Zahid Raza; Juan LG Guirao; Ghada Bassioni; Zahid Raza; Juan LG Guirao; Ghada Bassioni

doi:10.3934/mbe.2022583

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 12500-12517. doi: 10.3934/mbe.2022583

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The comparative analysis of two molecular indices in random polyphenyl and spiro chains

1.
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, UAE
2.
Departamento de Matematica Aplicada y Estadistica Universidad Politecnica de Cartagena, Hospital de Marina, Murcia 30203, Spain
3.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
4.
Department of Chemistry, Faculty of Engineering Ain Shams University, Cairo, Egypt
Academic editor: José M. Rodríguez

Received: 14 June 2022 Revised: 03 August 2022 Accepted: 08 August 2022 Published: 26 August 2022

Zagreb indices are well-known and historical indices that are very useful to calculate the properties of compounds. In the last few years, various kinds of Zagreb and Randic indices are investigated and defined to fulfil the demands of various engineering applications. Phenylenes are a class of conjugated hydrocarbons composed of a special arrangement of six- and four-membered rings. This special chain, produced by zeroth-order Markov process has been commonly appeared in the field of pharmacology and materials. Here, we compute the expected values of a multiplicative versions of the geometric arithmetic and atomic bond connectivity indices for these special hydrocarbons. Moreover, we make comparisons in the form of explicit formulae and numerical tables between the expected values of these indices in the random polyphenyl $ \mathbb{P}_n $ and spiro $ \mathbb{S}_n $ chains.
- atomic bond connectivity index,
- geometric arithmetic index,
- expected values,
- random polyphenyl chain,
- spiro chains,
- comparisons
Citation: Zahid Raza, Juan LG Guirao, Ghada Bassioni. The comparative analysis of two molecular indices in random polyphenyl and spiro chains[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12500-12517. doi: 10.3934/mbe.2022583

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Abstract

Zagreb indices are well-known and historical indices that are very useful to calculate the properties of compounds. In the last few years, various kinds of Zagreb and Randic indices are investigated and defined to fulfil the demands of various engineering applications. Phenylenes are a class of conjugated hydrocarbons composed of a special arrangement of six- and four-membered rings. This special chain, produced by zeroth-order Markov process has been commonly appeared in the field of pharmacology and materials. Here, we compute the expected values of a multiplicative versions of the geometric arithmetic and atomic bond connectivity indices for these special hydrocarbons. Moreover, we make comparisons in the form of explicit formulae and numerical tables between the expected values of these indices in the random polyphenyl $ \mathbb{P}_n $ and spiro $ \mathbb{S}_n $ chains.

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