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

Abstract

Let $\mathcal{C}_{n,k}$ be the family of all cacti with $k$ cycles and $n\geq4$ vertices. In the present note, the element of the class $\mathcal{C}_{n,k}$ having minimum augmented Zagreb index ($AZI$) is characterized. Moreover, some structural properties of the graph(s) having maximum $AZI$ value over the collection $\mathcal{C}_{n,0}$, are also reported.