Analysis of Eigenvalues for Molecular Structures  

作　　者：Muhammad Haroon Aftab Kamel Jebreen Mohammad Issa Sowaity Muhammad Hussain 

机构地区：[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

出　　处：《Computers, Materials & Continua》2022年第10期1225-1236,共12页计算机、材料和连续体（英文）

摘　　要：In this article,we study different molecular structures such as Polythiophene network,PLY(n)for n=1,2,and 3,Orthosilicate(Nesosilicate)SiO4,Pyrosilicates(Sorosilicates)Si2O7,Chain silicates(Pyroxenes)(SiO3)n,and Cyclic silicates(Ring Silicates)Si3O9 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)SiO4,Pyrosilicates(Sorosilicates)Si2O7,Chain silicates(Pyroxenes)(SiO3)n,and Cyclic silicates(Ring Silicates)Si3O9 generally have two same eigenvalues.Adjacency matrices have great importance in the field of computer science.

关 键 词：Vertex degree EDGES EIGENVALUES characteristics polynomials adjacency matrices graphical model GENETICS POLYTHIOPHENE SILICATES 

分 类 号：O15[理学—数学]