Analysis of Eigenvalues for Molecular Structures

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.