Complete solution to a conjecture on Randić index

For a graph G  , the Randić index R(G)R(G) of G   is defined by R(G)=∑u,v1d(u)d(v), where d(u)d(u) is the degree of a vertex u and the summation runs over all edges uv of G  . Let G(k,n)G(k,n) be the set of connected simple graphs of order n with minimum degree k  . Bollobás and Erdős once asked for finding the minimum value of the Randić index among the graphs in G(k,n)G(k,n). There have been many partial solutions for this question. In this paper we give a complete solution to the question.