Zhang-Zhang polynomial and some of its applications

Abstract

The Chinese mathematicians Heping Zhang and Fuji Zhang conceived a combinatorial polynomial associated with benzenoid molecules. This “Zhang–Zhang polynomial” contains information on both Kekul´e– and Clar–structure–based characteristics of the underlying benzenoid molecule. We first explain the definition of the Zhang– Zhang polynomial (and the theoretical concepts on which it is based), and then point out some of its applications to resonance energies. A peculiar discovery made by means of the Zhang–Zhang polynomial is that there are substantial differences between the structure dependence of the Dewar resonance energy and the topological resonance energy