Sharp bounds for the general Randić index r-1 of a graph

Abstract

Let G be an undirected simple, connected graph with n ≥ 3 vertices and m edges, with vertex degree sequence d1 ≥ d2 ≥ ⋯ ≥ dn. The general Randić index is defined by (Equation presented). Lower and upper bounds for R-1 are obtained in this paper.