Mathematical aspects and topological properties of two chemical networks

Ali Al Khabyah; Ali Al Khabyah

doi:10.3934/math.2023230

AIMS Mathematics

2023, Volume 8, Issue 2: 4666-4681. doi: 10.3934/math.2023230

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Research article

Mathematical aspects and topological properties of two chemical networks

Ali Al Khabyah ^,

Department of Mathematics, College of Science, Jazan University, New Campus, Jazan 2097, Saudi Arabia

Received: 12 October 2022 Revised: 06 November 2022 Accepted: 15 November 2022 Published: 06 December 2022
MSC : 05C09, 05C92

Graphs give a mathematical model of molecules, and thery are used extensively in chemical investigation. Strategically selections of graph invariants (formerly called "topological indices" or "molecular descriptors") are used in the mathematical modeling of the physio-chemical, pharmacologic, toxicological, and other aspects of chemical compounds. This paper describes a new technique to compute topological indices of two types of chemical networks. Our research examines the mathematical characteristics of molecular descriptors, particularly those that depend on graph degrees. We derive a compact mathematical analysis and neighborhood multiplicative topological indices for product of graphs ($ \mathcal{L} $) and tetrahedral diamond lattices ($ \Omega $). In this paper, the fifth multiplicative Zagreb index, the general fifth multiplicative Zagreb index, the fifth multiplicative hyper-Zagreb index, the fifth multiplicative product connectivity index, the fifth multiplicative sum connectivity index, the fifth multiplicative geometric-arithmetic index, the fifth multiplicative harmonic index and the fifth multiplicative redefined Zagreb index are determined. The comparison study of these topological indices is also discussed.
- neighborhood multiplicative topological indices,
- product of graph,
- tetrahedral diamond lattices,
- mathematical model,
- molecular graphs
Citation: Ali Al Khabyah. Mathematical aspects and topological properties of two chemical networks[J]. AIMS Mathematics, 2023, 8(2): 4666-4681. doi: 10.3934/math.2023230

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Abstract

Graphs give a mathematical model of molecules, and thery are used extensively in chemical investigation. Strategically selections of graph invariants (formerly called "topological indices" or "molecular descriptors") are used in the mathematical modeling of the physio-chemical, pharmacologic, toxicological, and other aspects of chemical compounds. This paper describes a new technique to compute topological indices of two types of chemical networks. Our research examines the mathematical characteristics of molecular descriptors, particularly those that depend on graph degrees. We derive a compact mathematical analysis and neighborhood multiplicative topological indices for product of graphs ($ \mathcal{L} $) and tetrahedral diamond lattices ($ \Omega $). In this paper, the fifth multiplicative Zagreb index, the general fifth multiplicative Zagreb index, the fifth multiplicative hyper-Zagreb index, the fifth multiplicative product connectivity index, the fifth multiplicative sum connectivity index, the fifth multiplicative geometric-arithmetic index, the fifth multiplicative harmonic index and the fifth multiplicative redefined Zagreb index are determined. The comparison study of these topological indices is also discussed.

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