A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles

Recent studies show that augmented Zagreb index (AZI) possess the best correlating ability among various well known topological indices for predicting the certain physicochemical properties of particular types of molecules. Hence, it is meaningful to study the mathematical properties of AZI, especially bounds and characterization of the extremal elements among well known graph families. For, n >= 4, let C-n,C-k be the collection of all cacti with k cycles and n vertices. In this note, the element of C-n,C-k having the minimum AZI is characterized. Some structural properties of the graph(s) having the maximum AZI over the collection C-n,C-0 are also reported.