Upper Bounds of AZI and ABC Index for Transformed Families of Graphs

Muhammad Hussain,Sultan Almotairi,Muhammad Asif,Ashit Kumar Dutta,Abdul Qadeer Khan

doi:10.1155/2022/4152854

Abstract

Topological index is a mapping which corresponds underlying graph with a numeric value and invariant up to all the isomorphisms of graph. Our study is based on a partial open question regarding topological indices: for which members of n-vertex graph family, certain index has minimum or maximum value? In this work, we answered the above-mentioned question regarding AZI and ABC for transformed families of graphs Γ n k , l and A α Γ n k , l . We investigated the fact of pendent paths and the transformation A α over these indices and developed the tight upper bounds regarding these families of graphs. Moreover, we characterized transformed graphs associated with maximum values of these indices.

Highlights

Nowadays, graph theory has potential applications in different fields of science
Graph theory has potential applications in different fields of science. It is especially used for theoretical study of chemical compounds in chemistry. is area of study named as chemical graph theory deals with the problems related to the properties in chemistry
Cheminformatics is comparatively the latest area of information technology which comprises chemistry, mathematics, and other informational sciences that concentrate on gathering, storing, treating, and examining chemical data. ere are many theoretical molecular descriptors in literature used to predict properties of chemical compounds

Summary

Introduction

Graph theory has potential applications in different fields of science. It is especially used for theoretical study of chemical compounds in chemistry. is area of study named as chemical graph theory deals with the problems related to the properties in chemistry. We studied ABC index and AZI for transformed graphs Γkn,l and Aα(Γkn,l) under the fact of transformation Aα, 0 ≤ α ≤ l − 2. Let Aα; 0 ≤ α ≤ l − 2 be the transformation defined over pendent paths attached with the graph [38].

Results

Conclusion