Randić structure of a graph

Abstract

AbstractLet G be a collection of graphs with n vertices. We present a simple description of [G]χ={H∈G:χ(H)=χ(G)} where χ denotes the Randić index. We associate to G a Q-linear map ρ:Qm→Qk (for some integers k,m depending on G) such that the kernel of ρ contains the necessary information to describe [G]χ in terms of linear equations. These results provide precise tools for analyzing the behavior of χ on a collection of graphs