Topological properties of reverse-degree-based indices for sodalite materials network

Koam, Ali N. A.; Ansari, Moin A.; Haider, Azeem; Ahmad, Ali; Azeem, Muhammad

doi:10.1016/j.arabjc.2022.104160

Cited by 7 publications

(2 citation statements)

References 41 publications

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“…• Entropy of atom-bond connectivity index [42,43] l ABC ðGÞ ¼ À 1 ABCðGÞ log Y ab2EðGÞ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi…”

Section: Methodology Of Proposed Workunclassified

Edge valency-based entropies of tetrahedral sheets of clay minerals

et al. 2023

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Humanity has always benefited from an intercapillary study in the quantification of natural occurrences in mathematics and other pure scientific fields. Graph theory was extremely helpful to other studies, particularly in the applied sciences. Specifically, in chemistry, graph theory made a significant contribution. For this, a transformation is required to create a graph representing a chemical network or structure, where the vertices of the graph represent the atoms in the chemical compound and the edges represent the bonds between the atoms. The quantity of edges that are incident to a vertex determines its valency (or degree) in a graph. The degree of uncertainty in a system is measured by the entropy of a probability. This idea is heavily grounded in statistical reasoning. It is primarily utilized for graphs that correspond to chemical structures. The development of some novel edge-weighted based entropies that correspond to valency-based topological indices is made possible by this research. Then these compositions are applied to clay mineral tetrahedral sheets. Since they have been in use for so long, corresponding indices are thought to be the most effective methods for quantifying chemical graphs. This article develops multiple edge degree-based entropies that correlate to the indices and determines how to modify them in order to assess the significance of each type.

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Section: Methodology Of Proposed Workunclassified

Edge valency-based entropies of tetrahedral sheets of clay minerals

et al. 2023

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“…A handbook of this mathematical tool can be found in [30], upper bounds of Zagreb indices in [31], and a discussion on the general Zagreb index in terms of unicyclic graphs is detailed in [32]. For some computational work of topological indices, see [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach for Extremal General Exponential Multiplicative Zagreb Indices

Ismail

Azeem

Shang

et al. 2023

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The study of the maximum and minimal characteristics of graphs is the focus of the significant field of mathematics known as extreme graph theory. Finding the biggest or smallest graphs that meet specified criteria is the main goal of this discipline. There are several applications of extremal graph theory in various fields, including computer science, physics, and chemistry. Some of the important applications include: Computer networking, social networking, chemistry and physics as well. Recently, in 2021 exponential multiplicative Zagreb indices were introduced. In generalization, we introduce the generalized form of exponential multiplicative Zagreb indices for α∈R+\{1}. Furthermore, to see the behaviour of generalized first and second exponential Zagreb indices for α∈R+\{1}, we used a transformation method. In term of the two newly developed generalized exponential multiplicative Zagreb indices, we will investigate the extremal bicyclic, uni-cyclic and trees graphs. Four graph transformations are used and some bounds are presented in terms of generalized exponential multiplicative Zagreb indices.

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