Degree-Based Topological Indices of Generalized Subdivision Double-Corona Product

Ying Wang,Adnan Aslam,Hamideh Aram,Muhammad Waheed,Syed Mazhar Shah,Muhammad Kamran Jamil,Hani Shaker

doi:10.1155/2022/3119739

Abstract

Graph operations play an important role in constructing complex network structures from simple graphs. Computation of topological indices of these complex structures via graph products is an important task. In this paper, we generalized the concept of subdivision double-corona product of graphs and investigated the exact expressions of the first and second Zagreb indices, first reformulated Zagreb index, and forgotten topological index (F-index) of this graph operation.

Highlights

In mathematics [1, 2], graph theory is the study of graphs which are mathematical structures used to model pairwise connection between objects
Any problem which includes graph structure can be solved by using the graph theoretical approach. is enables researchers to apply graph theory in various fields such as software engineering, biology, chemistry, and operation research
For any vertex p ∈ V(Υ), the degree of vertex p is the number of edges incident on the vertex p, and it is written as dΥ(p) or d(p). e subdivision of the graph Υ is denoted by S(Υ) and is obtained by inserting a new vertex on every edge of Υ

Summary

Introduction

In mathematics [1, 2], graph theory is the study of graphs which are mathematical structures used to model pairwise connection between objects. Topological index is called a molecular structure descriptor or graph theoretical descriptor [4]. E first and second Zagreb indices of a graph Υ are defined as Let X ⊆ V(Υ1) and Y ⊆ V(Υ2); the generalized subdivision double corona is denoted by Υ(S) ∘ 􏼈Υ1(X), Υ2(Y)􏼉 and is obtained by taking one copy of S(Υ), r copies of Υ1, and s copies of Υ2 and by joining the i-th old vertex of S(Υ) to every vertex of X of the i-th copy of Υ1 and j-th new vertex of S(Υ) to every vertex of Y of the j-th copy of Υ2.

Results

Conclusion