Randic Structure of a Graph

Let 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.