Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

Zhen Wang,Adnan Asghar,Maria Naseem,Faryal Chaudhry

doi:10.1155/2020/9805829

Zhen Wang, Adnan Asghar + Show 2 more

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https://doi.org/10.1155/2020/9805829

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Abstract

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. Topological indices help us collect information about algebraic graphs and give us mathematical approach to understand the properties of algebraic structures. With the help of topological indices, we can guess the properties of chemical compounds without performing experiments in wet lab. There are more than 148 topological indices in the literature, but none of them completely give all properties of under study compounds. Together, they do it to some extent; hence, there is always room to introduce new indices. In this paper, we present first and second reserve Zagreb indices and first reverse hyper-Zagreb indices, reverse GA index, and reverse atomic bond connectivity index for the crystallographic structure of molecules. We also present first and second reverse Zagreb polynomials and first and second reverse hyper-Zagreb polynomials for the crystallographic structure of molecules.

Highlights

Topological indices enable us to collect information about algebraic structures and give us a mathematical approach to understand the properties of algebraic structures
A molecular graph is a simple graph in which atoms and bonds are represented by vertex and edge sets, respectively. e vertex degree is the number of edges attached to that vertex [10,11,12,13,14,15,16]. e maximum degree of vertex among the vertices of a graph is denoted by Δ(G)
Graph theory in general is the study of different properties of objects but it tells us about objects having same properties as investigating object. ese properties of different objects are of main interest

Summary

Introduction

Topological indices enable us to collect information about algebraic structures and give us a mathematical approach to understand the properties of algebraic structures. E first and second reverse Zagreb indices are as follows: (1) CM1(Cu2O) 32mαt + 20mα + 20mt + 20αt + 36 − 28m − 28α − 28t (ii) e second reverse Zagreb polynomial for Cu2O, with m, α, t ≥ 1, is given as follows: CM2 Cu2O, x􏼁 􏽘 x(cu.cv)

Results

Conclusion