Further Results on the Augmented Zagreb Index

Fuqin Zhan

Abstract: The augmented Zagreb index of a simple connected graph is defined as , where is the degree of vertex in . A connected graph is called a quasi-tree graph if there exists a vertex such that is a tree. A connected graph is a cactus if any two of its cycles have at most one common vertex. In this paper, we determine the smallest and the second-smallest AZI indices of quasi-tree graphs and the minimal AZI index in the class of all cacti graphs with vertices and cycles.