Vertex-degree-based topological indices over graphs (2014)
Given a graph G with n vertices, a vertex-degree-based topological index is defined from a set of real numbers {ϕij} as T I (G) = mij (G) ϕij , where mij (G) is the number of edges between vertices of degree i and degree j, and the sum runs over all 1 ≤ i ≤ j ≤ n − 1. In this general setting, we find bounds for the values of T I over the set Gn of graphs with n (non-isolated) vertices. As an application we find the extremal values of the general Randi´c index Rt when t ∈ −1, −1 2 , an open problem proposed in [13].