Complete solution to a conjecture on Randi? index ?
For a graph G , the Randi? index R(G) R ( G ) of G  is defined by R ( G ) = ? u , v 1 d ( 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 . Bollobs and Erd?s once asked for finding the minimum value of the Randi? 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.
randi? index simple graph minimum degree minimum value