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

Akbar Ali, Akhlaq A. Bhatti


Recent studies show that augmented Zagreb index (AZI) possess the best correlating ability among the various well known topological indices for predicting the certain physicochemical properties ofparticular types of molecules. Hence it is meaningful to study the mathematical properties of AZI, especially bounds and characterization of the extremal elements of well known graph families. Let C_{n,k} be the family of all cacti with k cycles and n>3 vertices. In the present note, the element of the class C_{n,k} having minimum AZI is characterized. Moreover, some structural properties of the graph(s) having maximum AZI value over the collection C_{n,0} are also reported.


Augmented Zagreb index; cactus graph; topological index.

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