Sharp Bounds for Kulli-Basava Indices of Graphs

Abstract

In this paper, we establish formulas and sharp bounds for general Kulli-Basava indices and characterize graphs that attain these bounds. These indices have been shown to possess strong discriminating power for distinguishing nonisomorphic chemical structures. They are based on the edge neighborhood degrees of vertices in a graph. We also establish bounds for several classes of graphs, including triangle- and quadrangle-free graphs and graphs with a prescribed clique number. The formulas and bounds depend on the numbers of vertices and edges, the minimum and maximum edge neighborhood degrees, and the first Zagreb index.