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Analysis of Eigenvalues for Molecular Structures

Computers, Materials & Continua 2022年第10期73卷 1225-1236页

作者： Muhammad Haroon Aftab kamel jebreen Mohammad Issa Sowaity Muhammad Hussain Department of Mathematics and Statistics The University of LahoreLahore54000Pakistan Department of Mathematics An-Najah National UniversityNablusP400Palestine Department of Mathematics Palestince Polytechnic UniversityHebronP766Palestine Department of Mathematics Comsats University IslamabadLahore CampusLahore54000Pakistan

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 *** convert the general structures of these chemical networks in to mathematical graphical *** 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 *** matrices obtained from these simple undirected graphs are *** also label the molecular structures by assigning different *** graphs have also been studied for *** a connected graph,the eigenvalue that shows its peak point(largest value)obtained from the adjacency matrix has multiplicity ***,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 *** 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

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An Approximation for the Entropy Measuring in the General Structure of SGSP_(3)

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Computers, Materials & Continua 2022年第12期73卷 4455-4463页

作者： Zeeshan Saleem Muftiand Muhammad Hussain kamel jebreen Muhammad Haroon Aftab Mohammad Issa Sowaity Zeeshan Saleem Mufti Muhammad Hussain Biostatistics and Clinical Research Department University Hospital LariboisièreAP-HPUniversite’de ParisParis75010France Department of Mathematics An-Najah National UniversityNablusP400Palestine Department of Mathematics Palestine Technical University-KadoorieHebronP766Palestine Department of Mathematics and Statistics the University of LahoreLahore54000Pakistan Department of Mathematics Palestine Polytechnic UniversityHebronP766Palestine Department of Mathematics COMSATS University IslamabadLahore campusLahore54000Pakistan

In this article,we calculate various topological invariants such as symmetric division degree index,redefined Zagreb index,VL index,first and second exponential Zagreb index,first and second multiplicative exponential Zagreb indices,symmetric division degree entropy,redefined Zagreb entropy,VL entropy,first and second exponential Zagreb entropies,multiplicative exponential Zagreb *** take the chemical compound named Proanthocyanidins,which is a very useful polyphenol in human’s *** are very beneficial for one’s *** chemical compounds are extracted from grape *** are tremendously anti-inflammatory.A subdivision formof this compound is presented in this *** compound named subdivided grape seed Proanthocyanidins is abbreviated as SGSP_(3).This network SGSP_(3),is converted and modeled into its mathematical graphical formation with the support of the latest mathematical *** have also developed many closed formulas for the measurement of entropy for the general chemical structure of the subdivided grape seed Proanthocyanidins *** achieved outcomes can be correlated with the chemical version of SGSP_(3) to get a better understanding of its biological as well as physical features.

关键词： Symmetric division degree redefined Zagreb VL index exponential multiplicative Zagreb subdivided grape seed Proanthocyanidins graphical model genetics entropy

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