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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 ($AZI$) ischaracterized. Moreover, some structural properties of the graph(s) havingmaximum $AZI$ value over the collection $\mathcal{C}_{n,0}$, are also reported.

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