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

Abstract

Let C n,k be the family of all cacti with k cycles and n ≥ 4 vertices. In the present note, the element of the class 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 C n,0 , are also reported.