More ordering on the difference between atom-bond connectivity index and Randić index of binary trees

Abstract

Let G be a simple graph with vertex set V(G) and edge set E(G). The atom-bond connectivity and Randić index of graph G are defined as and , respectively, where du denotes the degree of vertex u in G. Let ABC – R denotes the difference between ABC index and R index. In this paper, we present a further ordering for the ABC – R indices, and determine the fourth, the fifth, the sixth, the seventh and the eighth maximum binary trees with respect to the ABC – R values.