Cluj and Related Polynomials Applied in Correlating Studies

A counting polynomial P(G,x) is a description of a graph property P(G) in terms of a sequence of numbers so that the exponents express the extent of its partitions while the coefficients are related to the frequency of the occurrence of partitions. Basic definitions and properties of Cluj counting polynomials CJ(G,x) and their relation with Omega(G,x) and NOmega(G,x) polynomials are presented. Analytical relations for the calculation of such polynomials and their single-number descriptors in some classes of planar polyhexes are derived. The ability of these descriptors to predict the boiling point, chromatographic retention index, and resonance energy for some planar polyhex compounds, as well as the toxicity of a set of dibenzofurans, is demonstrated.