The vertex Zagreb indices of some graph operations

De, Nilanjan

doi:10.15330/cmp.8.2.215-223

Cited by 7 publications

(5 citation statements)

References 26 publications

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“…• The product of networks are mostly used in CGT for chemical structures such as carbonnano tube, bottleneck graph, linear polyomino chain, fence, closed fence, alkane and cyclohexane ( [1], [8], [13], [46]).…”

Section: Uses and Significance For Product Of Networkmentioning

confidence: 99%

Comparison Between Connection Based Modified Indices and Coindices for Product of Networks

2022

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Topological indices (TIs) are functional tools which correlate with a computational value through a undirected, finite and simple networks. Many physicochemical properties and chemical reactions are studied with the help of these TIs. Recently, they are commonly used in the behavior of quantitative structures activity as well as property relationships. In 1972, connection number based TIs are studied by Gutman and Trinajstić to calculate the entire π-electron energy of the alternant hydrocarbons. Moreover, the data provided by the website http://www.moleculardescriptors.eu shows that the relations between Zagreb indices and connection based indices that provide the better absolute values of the correlation coefficients for the thirteen physicochemical properties of the octane isomers. In this paper, we discuss the two invariants which are modified indices and modified coindices based on connection number of the resultant networks obtained by the different operations of product such as lexicographic and corona. For the molecular networks such as fence, closed fence, alkene and cycloalkane are depicted in the consequences of the obtained results. The comparisons between two invariants of the aforemention molecular networks are also presented through tables and graphical depictions. In addition, the uses and significance related to product of networks are also included. "INDEX TERMS "Indices and coindices; Product of networks; Connection number."

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Section: Uses and Significance For Product Of Networkmentioning

confidence: 99%

Comparison Between Connection Based Modified Indices and Coindices for Product of Networks

2022

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“…e author of [35] computed the forgotten topological index of different corona products of graphs, and the authors of [36] gave the exact expressions of Zagreb indices of the generalized hierarchical product of graphs. For more discussion and results, we refer to [37,38].…”

Section: Introductionmentioning

confidence: 99%

Topological Descriptors for the Metal Organic Network and Its Structural Properties

Ahmad

Elahi

Azeem

et al. 2022

Journal of Mathematics

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Metal organic structures and networks are extensively studied in modern chemistry. These networks are extremely adaptable and useful in a variety of fields. Metal organic networks are thought to be the home of gases, and this structure is also engaged in gas purification and separation. The fact that they have so much utility and applicability stems from that they have so many distinct properties, such as exchanging ions and altering organic ligands. This structure’s chemical and physical properties are considered. There are extensive, time-consuming, and costly experiments available to investigate these physical and chemical properties. To avoid these complex experiments and tests, a mathematical study provides approximate details of these chemical and physical behaviors of a structure, which is known as topological descriptors. In this work, we discussed the metal organic network’s line graph and studied the structural properties of the resulted network with the help of topological descriptors.

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“…In [16], Das et al found some upper bounds for multiplicative Zagreb indices of some graph operations and Azari et al in [17], derived explicit formulae for computing the eccentric-distance sum of different graph operations. Recently, De computes the vertex Zagreb indices of different graph operations in [18]. For more results, interested readers are referred to the papers [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs

De¹

2018

Open J. Math. Sci

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The generalized hierarchical product of graphs was introduced by L. Barriére et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb lattice, hexagonal chain, molecular graph of truncated cube, dimer fullerene, zig-zag polyhex nanotube and dicentric dendrimers are computed.

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The vertex Zagreb indices of some graph operations

Cited by 7 publications

References 26 publications

Comparison Between Connection Based Modified Indices and Coindices for Product of Networks

Comparison Between Connection Based Modified Indices and Coindices for Product of Networks

Topological Descriptors for the Metal Organic Network and Its Structural Properties

Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs

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