Three New/Old Vertex-Degree-Based Topological Indices

Three vertex-degree-based graph invariants are presented, that earlier have been considered in the chemical and/or mathematical literature, but that evaded the attention of most mathematical chemists. These are the reciprocal Randio index (RR), the reduced second Zagreb index RM2, and the reduced reciprocal Randlo index (RRR). If d(1), d(2), ..., d(n) are the degrees of the vertices of the graph G = (V, E), then RR = Sigma(ij is an element of E) root d(i)d(j), RM2 = Sigma(ij is an element of E)(d(i) - 1)(d(j) - 1), RRR = Sigma(ij is an element of E)root(d(i) - 1)(d(j) - 1). We outline the literature sources of these topological indices, their main mathematical properties, and establish their correlating abilities w.r.t. characteristic physico-chemical properties of allianes.