Characteristic and matching polynomials of benzenoid hydrocarbons

Abstract

The characteristic and matching polynomials of the molecular graph of a benzenoid hydrocarbon are examined and a number of results proved for their coefficients. These results are then applied to the theory of topological resonance energy (TRE). It is demonstrated that all benzenoid hydrocarbons have positive TRE values and that the TRE model leads to absurd results in the case of polyradical benzenoid systems.