New Bounds for the Randić Index of Graphs

Abstract

The Randić index of a graph G is defined as the sum of weights 1/dudv over all edges uv of G, where du and dv are the degrees of the vertices u and v in G, respectively. In this paper, we will obtain lower and upper bounds for the Randić index in terms of size, maximum degree, and minimum degree. Moreover, we obtain a generally lower and a general upper bound for the Randić index.