Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

Muhammad Asad Ali,Muhammad Shoaib Sardar,Dalal Alrowaili,Imran Siddique,Muhammad Imran

doi:10.1155/2021/7057412

Muhammad Asad Ali, Muhammad Shoaib Sardar + Show 3 more

Open Access

https://doi.org/10.1155/2021/7057412

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Abstract

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1 and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

Highlights

Introduction and PreliminariesFor undetermined notations and terminologies, we recommend Robin J
Contains edges of type E(4,4) and E(4,4p), and Table 1 presents the edges of these types
We recommend the readers to compute the topological indices for double and strong double graphs of some other classes of graphs or networks

Summary

Introduction and Preliminaries

For undetermined notations and terminologies, we recommend Robin J. Assume that G is a simple graph that has no multiple edges and loops. V(G) and E(G) are the vertex and edge sets of graph G, respectively. Vertex degree is the number of edges joining to a vertex in a graph G. A vertex degree is indicated by dr {r ∈ V(G)} and Sr 􏽐s∈NG(r)ds, where NG(r) {s ∈ V(G) | rs ∈ E(G)}. E following lemma is useful for computing the total number of edges in a graph G. is is called the handshake lemma and was observed by Lenford Euler in 1736. Ese topological indices analyse the structure of any finite graph and are based on mathematical equations. E first multiplicative-Zagreb index (PM1) can be written in the sum of the edges [16] of G: PM1(G) 􏽙 dr + ds􏼁. Where Sr is summation of degrees of all neighbor of vertex r, and the same for Ss

Number of edges

Dutch is

Dutch indeg