  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.
