On the Augmented Zagreb Index

TL;DR

This paper investigates the mathematical properties of the augmented Zagreb index (AZI), establishing bounds for specific graph classes and a Nordhaus-Gaddum-type result, enhancing its application in chemical graph theory.

Contribution

It provides new mathematical bounds for AZI on bicyclic and unicyclic graphs and introduces a Nordhaus-Gaddum-type inequality for connected graphs with connected complements.

Findings

Established tight bounds for AZI on bicyclic graphs.

Established tight bounds for AZI on unicyclic graphs.

Derived a Nordhaus-Gaddum-type inequality for AZI.

Abstract

Topological indices play an important role in mathematical chemistry especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). Recent research indicates that the augmented Zagreb index (AZI) possess the best correlating ability among several topological indices. The main purpose of the current study is to establish some mathematical properties of this index, or more precisely, to report tight bounds for the AZI of chemical bicyclic and chemical unicyclic graphs. A Nordhaus-Gaddum-type result for the AZI (of connected graph whose complement is connected) is also derived.