Three new/old vertex-degree-based topological indices

Abstract

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 Randić index (\(RR\)), the reduced second Zagreb index \(RM_2\), and the reduced reciprocal Randić index (\(RRR\)). If \(d_1, d_2,\ldots, d_n\) are the degrees of the vertices of the graph \(G = (V,E)\), then \[ RR = \sum_{ij\in E} \sqrt{d_i\,d_j} \quad RM_2 = \sum_{ij\in E} (d_i - 1)(d_j - 1) \quad RRR = \sum_{ij\in E} \sqrt{(d_i - 1)(d_j - 1)} \ . \] 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 alkanes.