One of the most recent developments in the field of graph theory is the analysis of networks such as Butterfly networks,Benes networks,Interconnection networks,and David-derived networks using graph theoretic paramete...One of the most recent developments in the field of graph theory is the analysis of networks such as Butterfly networks,Benes networks,Interconnection networks,and David-derived networks using graph theoretic parameters.The topological indices(TIs)have been widely used as graph invariants among various graph theoretic tools.Quantitative structure activity relationships(QSAR)and quantitative structure property relationships(QSPR)need the use of TIs.Different structure-based parameters,such as the degree and distance of vertices in graphs,contribute to the determination of the values of TIs.Among other recently introduced novelties,the classes of ev-degree and ve-degree dependent TIs have been extensively explored for various graph families.The current research focuses on the development of formulae for different ev-degree and ve-degree dependent TIs for s−dimensional Benes network and certain networks derived from it.In the end,a comparison between the values of the TIs for these networks has been presented through graphical tools.展开更多
Topological indices enable to gather information for the underlying topology of chemical structures and networks.Novel harmonic indices have been defined recently.All degree based topological indices are defined by us...Topological indices enable to gather information for the underlying topology of chemical structures and networks.Novel harmonic indices have been defined recently.All degree based topological indices are defined by using the classical degree concept.Recently two novel degree concept have been defined in graph theory:ve-degree and evdegree.Ve-degree Zagreb indices have been defined by using ve-degree concept.The prediction power of the ve-degree Zagreb indices is stronger than the classical Zagreb indices.Dominating oxide,silicate and oxygen networks are important network models in view of chemistry,physics and information science.Physical and mathematical properties of dominating oxide,silicate and oxygen networks have been considerably studied in graph theory and network theory.Topological properties of the dominating oxide,silicate and oxygen networks have been intensively investigated for the last few years period.In this study we examined,the first,the fifth harmonic and ev-degree topological indices of dominating oxide(DOX),regular triangulene oxide network(RTOX)and dominating silicate network(DSL).展开更多
In quantitative structure-property relationship(QSPR)and quantitative structure-activity relationship(QSAR)studies,computation of topological indices is a vital tool to predict biochemical and physio-chemical properti...In quantitative structure-property relationship(QSPR)and quantitative structure-activity relationship(QSAR)studies,computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures.Numerous topological indices have been inaugurated to describe different topological features.The ev and ve-degree are recently introduced novelties,having stronger prediction ability.In this article,we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of Si_(2)C_(3)−I[a,b].展开更多
Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences.The dynamical arrangement of vertices and their associated edges make them flexible(like liquid)to attain the shape o...Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences.The dynamical arrangement of vertices and their associated edges make them flexible(like liquid)to attain the shape of any physical structure or phenomenon easily.In the field of ICT they are used to reflect distributed component and communication among them.Mathematical chemistry is another interesting domain of applied mathematics that endeavors to display the structure of compounds that are formed in result of chemical reactions.This area attracts the researchers due to its applications in theoretical and organic chemistry.It also inspires the mathematicians due to involvement of mathematical structures.Regular or irregular bonding ability of molecules and their formation of chemical compounds can be analyzed using atomic valences(vertex degrees).Pictorial representation of these compounds helps in identifying their properties by computing different graph invariants that is really considered as an application of graph theory.This paper reflects the work on topological indices such as ev-degree Zagreb index,the first ve-degree Zagrebindex,the first ve-degree Zagrebindex,the second ve-degree Zagreb index,ve-degree Randic index,the ev-degree Randic index,the ve-degree atom-bond connectivity index,the ve-degree geometric-arithmetic index,the ve-degree harmonic index and the ve-degree sum-connectivity index for crystal structural networks namely,bismuth tri-iodide and lead chloride.In this article we have determine the exact values of ve-degree and ev-degree based topological descriptors for crystal networks.展开更多
Chemical graph theory is a branch of mathematics which combines graph theory and chemistry.Chemical reaction network theory is a territory of applied mathematics that endeavors to display the conduct of genuine compou...Chemical graph theory is a branch of mathematics which combines graph theory and chemistry.Chemical reaction network theory is a territory of applied mathematics that endeavors to display the conduct of genuine compound frameworks.It pulled the research community due to its applications in theoretical and organic chemistry since 1960.Additionally,it also increases the interest the mathematicians due to the interesting mathematical structures and problems are involved.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.In this paper,we determined the newly introduced topological indices namely,first ve-degree Zagreb?index,first ve-degree Zagreb?index,second ve-degree Zagreb index,ve-degree Randic index,ve-degree atom-bond connectivity index,ve-degree geometric-arithmetic index,ve-degree harmonic index and ve-degree sum-connectivity index for honey comb derived network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure-activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.Also,we give the numerical and graphical representation of our outcomes.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.61702291)China Henan International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5.
文摘One of the most recent developments in the field of graph theory is the analysis of networks such as Butterfly networks,Benes networks,Interconnection networks,and David-derived networks using graph theoretic parameters.The topological indices(TIs)have been widely used as graph invariants among various graph theoretic tools.Quantitative structure activity relationships(QSAR)and quantitative structure property relationships(QSPR)need the use of TIs.Different structure-based parameters,such as the degree and distance of vertices in graphs,contribute to the determination of the values of TIs.Among other recently introduced novelties,the classes of ev-degree and ve-degree dependent TIs have been extensively explored for various graph families.The current research focuses on the development of formulae for different ev-degree and ve-degree dependent TIs for s−dimensional Benes network and certain networks derived from it.In the end,a comparison between the values of the TIs for these networks has been presented through graphical tools.
文摘Topological indices enable to gather information for the underlying topology of chemical structures and networks.Novel harmonic indices have been defined recently.All degree based topological indices are defined by using the classical degree concept.Recently two novel degree concept have been defined in graph theory:ve-degree and evdegree.Ve-degree Zagreb indices have been defined by using ve-degree concept.The prediction power of the ve-degree Zagreb indices is stronger than the classical Zagreb indices.Dominating oxide,silicate and oxygen networks are important network models in view of chemistry,physics and information science.Physical and mathematical properties of dominating oxide,silicate and oxygen networks have been considerably studied in graph theory and network theory.Topological properties of the dominating oxide,silicate and oxygen networks have been intensively investigated for the last few years period.In this study we examined,the first,the fifth harmonic and ev-degree topological indices of dominating oxide(DOX),regular triangulene oxide network(RTOX)and dominating silicate network(DSL).
文摘In quantitative structure-property relationship(QSPR)and quantitative structure-activity relationship(QSAR)studies,computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures.Numerous topological indices have been inaugurated to describe different topological features.The ev and ve-degree are recently introduced novelties,having stronger prediction ability.In this article,we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of Si_(2)C_(3)−I[a,b].
基金the Deanship of Scientific Research(DSR)at King Abdulaziz University,Jeddah,under Grant No.RG-29-135-38.
文摘Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences.The dynamical arrangement of vertices and their associated edges make them flexible(like liquid)to attain the shape of any physical structure or phenomenon easily.In the field of ICT they are used to reflect distributed component and communication among them.Mathematical chemistry is another interesting domain of applied mathematics that endeavors to display the structure of compounds that are formed in result of chemical reactions.This area attracts the researchers due to its applications in theoretical and organic chemistry.It also inspires the mathematicians due to involvement of mathematical structures.Regular or irregular bonding ability of molecules and their formation of chemical compounds can be analyzed using atomic valences(vertex degrees).Pictorial representation of these compounds helps in identifying their properties by computing different graph invariants that is really considered as an application of graph theory.This paper reflects the work on topological indices such as ev-degree Zagreb index,the first ve-degree Zagrebindex,the first ve-degree Zagrebindex,the second ve-degree Zagreb index,ve-degree Randic index,the ev-degree Randic index,the ve-degree atom-bond connectivity index,the ve-degree geometric-arithmetic index,the ve-degree harmonic index and the ve-degree sum-connectivity index for crystal structural networks namely,bismuth tri-iodide and lead chloride.In this article we have determine the exact values of ve-degree and ev-degree based topological descriptors for crystal networks.
文摘Chemical graph theory is a branch of mathematics which combines graph theory and chemistry.Chemical reaction network theory is a territory of applied mathematics that endeavors to display the conduct of genuine compound frameworks.It pulled the research community due to its applications in theoretical and organic chemistry since 1960.Additionally,it also increases the interest the mathematicians due to the interesting mathematical structures and problems are involved.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.In this paper,we determined the newly introduced topological indices namely,first ve-degree Zagreb?index,first ve-degree Zagreb?index,second ve-degree Zagreb index,ve-degree Randic index,ve-degree atom-bond connectivity index,ve-degree geometric-arithmetic index,ve-degree harmonic index and ve-degree sum-connectivity index for honey comb derived network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure-activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.Also,we give the numerical and graphical representation of our outcomes.
