Open Access

ARTICLE

Analysis of Eigenvalues for Molecular Structures

Muhammad Haroon Aftab¹, Kamel Jebreen^2,*, Mohammad Issa Sowaity³, Muhammad Hussain⁴

1 Department of Mathematics and Statistics, The University of Lahore, Lahore, 54000, Pakistan
2 Department of Mathematics, An-Najah National University, Nablus, P400, Palestine
3 Department of Mathematics, Palestince Polytechnic University, Hebron, P766, Palestine
4 Department of Mathematics, Comsats University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

* Corresponding Author: Kamel Jebreen. Email:

Computers, Materials & Continua 2022, 73(1), 1225-1236. https://doi.org/10.32604/cmc.2022.029009

Received 22 February 2022; Accepted 30 March 2022; Issue published 18 May 2022

Abstract

In this article, we study different molecular structures such as Polythiophene network, for and , Orthosilicate (Nesosilicate) , Pyrosilicates (Sorosilicates) , Chain silicates (Pyroxenes), and Cyclic silicates (Ring Silicates) for their cardinalities, chromatic numbers, graph variations, eigenvalues obtained from the adjacency matrices which are square matrices in order and their corresponding characteristics polynomials. We convert the general structures of these chemical networks in to mathematical graphical structures. We transform the molecular structures of these chemical networks which are mentioned above, into a simple and undirected planar graph and sketch them with various techniques of mathematics. The matrices obtained from these simple undirected graphs are symmetric. We also label the molecular structures by assigning different colors. Their graphs have also been studied for analysis. For a connected graph, the eigenvalue that shows its peak point (largest value) obtained from the adjacency matrix has multiplicity 1. Therefore, the gap between the largest and its smallest eigenvalues is interlinked with some form of “connectivity measurement of the structural graph”. We also note that the chemical structures, Orthosilicate (Nesosilicate) , Pyrosilicates (Sorosilicates) , Chain silicates (Pyroxenes) , and Cyclic silicates (Ring Silicates) generally have two same eigenvalues. Adjacency matrices have great importance in the field of computer science.

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Keywords

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