The Randić index of a graph G, denoted by R(G), is defined as the sum of 1/ √ d(u)d(v) over all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we partially solve two conjectures on the Randić index R(G) with relations to the diameter D(G) and the average distance μ(G) of a graph G. We prove that for any connected graph G of order n with minimum degree δ(G), if δ...

One of the useful indices in molecular topology is Randić index. The alternative double bonds andconjugation in the polyene compounds are one of the main properties in these compounds. Someof the molecular orbital and structural properties refer to this specialty, such as: molar absorptioncoefficient (εmax) , electrical conductivity and difference energy level of the HOMO and LUMOorbitals, etc....

The harmonic index is one of the most important indices in chemical and mathematical fields. It’s a variant of the Randić index which is the most successful molecular descriptor in structure-property and structureactivity relationships studies. The harmonic index gives somewhat better correlations with physical and chemical properties comparing with the well known Randić index. The harmonic ind...