Bounds on the Arithmetic-Geometric Index

José M Rodríguez,Eva Tourís,José L Sánchez,José M Sigarreta

doi:10.3390/sym13040689

José M Rodríguez, Eva Tourís + Show 2 more

Open Access

https://doi.org/10.3390/sym13040689

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Abstract

The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric index and characterize the extremal graphs with respect to them. Several bounds are based on other indices, such as the second variable Zagreb index or the general atom-bond connectivity index), and some of them involve some parameters, such as the number of edges, the maximum degree, or the minimum degree of the graph. In most bounds, the graphs for which equality is attained are regular or biregular, or star graphs.

Highlights

In chemical graph theory, a topological descriptor is a function that associates each molecular graph with a real value
An upper bound of AG that is based on the second variable Zagreb index M2a (Theorem 2)
An upper bound of AG based on the general atom-bond connectivity index ABCa (Theorem 4)

Summary

Introduction

A topological descriptor is a function that associates each molecular graph with a real value. If it correlates well with some chemical property, it is called a topological index. In [25,26,27,28], there are more bounds on the AG index and a discussion on the effect of deleting an edge from a graph on the arithmetic-geometric index. It is important to find lower bounds of AG that are greater than m With this aim, in this paper we obtain several new lower bounds of AG, which are greater than m, and we characterize the extremal graphs

Bounds Involving Other Indices

General Bounds on the AG Index

Conclusions