Abstract
Topological indices play an important role in Mathematical Chemistry, especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. Recent research indicates that to predict the certain physico-chemical properties of particular types of molecules, 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 AZI (of connected graph whose complement is connected) is also derived.