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 Cycli...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.展开更多
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...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 entropy.We take the chemical compound named Proanthocyanidins,which is a very useful polyphenol in human’s diet.They are very beneficial for one’s health.These chemical compounds are extracted from grape seeds.They are tremendously anti-inflammatory.A subdivision formof this compound is presented in this article.The 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 tools.We have also developed many closed formulas for the measurement of entropy for the general chemical structure of the subdivided grape seed Proanthocyanidins network.The 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.展开更多
文摘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.
基金Under the sponsor of Unitéde Recherche Clinique Lariboisière St-Louis(URC)Assistance Publique-Hoitaux de Paris 200,rue du Fbg Saint-Denis 75010 Paris.
文摘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 entropy.We take the chemical compound named Proanthocyanidins,which is a very useful polyphenol in human’s diet.They are very beneficial for one’s health.These chemical compounds are extracted from grape seeds.They are tremendously anti-inflammatory.A subdivision formof this compound is presented in this article.The 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 tools.We have also developed many closed formulas for the measurement of entropy for the general chemical structure of the subdivided grape seed Proanthocyanidins network.The 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.
