Three Topological Indices of Two New Variants of Graph Products

Muhammad Bilal,Muhammad Kamran Jamil,Muhammad Waheed,Abdu Alameri

doi:10.1155/2021/7724177

Abstract

Graph operations play an important role to constructing complex network structures from simple graphs, and these complex networks play vital roles in different fields such as computer science, chemistry, and social sciences. Computation of topological indices of these complex network structures via graph operation is an important task. In this study, we defined two new variants of graph products, namely, corona join and subdivision vertex join products and investigated exact expressions of the first and second Zagreb indices and first reformulated Zagreb index for these new products.

Highlights

The graph theory is the study of graphs which are mathematical structures used to model pairwise connection between objects. e graph theory is applied in the various fields such as computer science, biology, chemistry, social sciences, and operation research [1, 2]
For any vertex v ∈ V(G), the degree of vertex v is the number of edges incident on the vertex v, and it is written as dG(v) or d(v)
Topological index is a numeric value which is associated with a chemical structure of a certain chemical compound

Summary

Introduction

The graph theory is the study of graphs which are mathematical structures used to model pairwise connection between objects. e graph theory is applied in the various fields such as computer science, biology, chemistry, social sciences, and operation research [1, 2].Let G (V(G), E(G)) be a simple, connected graph with vertex set V(G) and edge set E(G). e number of vertices and number of edges are called the order n and size m, respectively, of the graph G. For a graph G, the first and second Zagreb indices are defined as Khalifeh et al [15] computed the first and second Zagreb indices of Cartesian product, composition, join, disjunction, and symmetric difference of graphs and applied the results on C4 tube, torus, and multiwalled polyhex nanotorus. E following lemmas are useful to obtain the exact expressions of topological indices of new variants of graph products.

Results

Conclusion