The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.

The topological structures of many social, biological, and technological systems can be characterized by the connectivity properties of the interaction pathways (edges) between system components (vertices) [1]. Starting with the Königsberg seven-bridge problem in 1736, graphs with bidirectional or symmetric edges have ideally epitomized structures of various complex systems, and have developed ...