A Unified Approach for Extremal General Exponential Multiplicative Zagreb Indices

Abstract

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.

Reverse-degree-based topological indices of two-dimensional coronene fractal structures

“…At the beginning of the literature review of the topic, we suggest seeing the articles purely related to the reverse degree-based topological descriptors [23][24][25], simple degree-based topological descriptors [26][27][28], related to the analysis of different medicines and chemical structures with respect to the topological descriptors [29][30][31], some topics very closed to the topological descriptors and graph theoretical parameters [32][33][34], topics based on the study of different chemical and computer networks related to the graph theoretical approach [35,36].…”

A comparison between certain graph parameters of biswapped networks and their maximal twin-preserving subgraphs with applications in determining complexity

“…The ZIs and RI, dependent on the ev-degree and ve-degree notations, are formulated in [26][27][28][29], and it was analysed that the predicting ability of ve-degree ZI was improved as compared to its classical version. Recently, the maximum variable exdeg index for conjugated tricyclic graphs [30], the Sombor index and degree-related properties of simplicial networks [31], a unified approach for extremal general exponential multiplicative ZIs [32] and the Gaussian Estrada index of graphs [33] are also notable additions to the study of TIs. For more developments on the study of TIs, see [34][35][36][37][38].…”