New Bounds for the Randić Index of Graphs

The Randić index of a graph G is defined as the sum of weights 1 / d u d v over all edges u v of G , where d u and d v 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.