Extremal Values of Variable Sum Exdeg Index for Conjugated Bicyclic Graphs

Muhammad Rizwan,Akhlaq Ahmad Bhatti,Ebenezer Bonyah,Muhammad Javaid,Haidar Ali

doi:10.1155/2021/4272208

Abstract

A connected graph G V , E in which the number of edges is one more than its number of vertices is called a bicyclic graph. A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set such that the number of vertices is two times its matching number. In this paper, we investigated maximum and minimum values of variable sum exdeg index, SEI a for bicyclic graphs with perfect matching for k ≥ 5 and a > 1 .

Highlights

A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set such that n 2m
Usually we can represent the molecular structure by graph, and, in these graphs, vertices correspond to atoms, whereas edges correspond to bonds [2]
Topological indices play a significant role in organic chemistry and in pharmacology to determine the extremal values of chemical structure because these extremal values of the chemical structure give information about the physicochemical properties of the related molecule

Summary

Introduction

A subset M(G) ⊂ E(G) is said to be m-matching in G if no two elements in M(G) are adjacent, where |M(G)| m. To better understand physicochemical properties of a chemical graph, nowadays researchers are using topological indices. Topological indices play a significant role in organic chemistry and in pharmacology to determine the extremal values of chemical structure because these extremal values of the chemical structure give information about the physicochemical properties of the related molecule. In 1972, for a molecule to calculate the total π-electron energy, the technique of sum of the squares of degrees (valencies) of the vertices (nodes) was used After that, this topological index was named Zagreb index and became very famous [9]. Regarding extremal graph theory in literature, upper and lower bounds for cyclic graphs have been investigated for many wellswotted molecular structure descriptors such as hyperZagreb index [10], variable sum exdeg index [11], and Zagreb indices [12]. We refer the readers to [13, 14] to see chemical application of this index

Some Known Results

From and a

We have

Conclusion