Extremal values for the variation of the Randić index of bicyclic graphs

Abstract

Let G be a connected graph of order n. The variation of the Randić index of G is defined as R′(G)= ∑uv∈E(G)1max{d(u),d(v)}, where the summation goes over all edges uv of G and d(u) is the degree of the vertex u in G. In this paper, among all bicyclic graphs of order n, the minimum and maximum values for R′ are determined, respectively.