Equivalence of the Generalized Zhang-Zhang Polynomial and the Generalized Cube Polynomial

In this paper we study the resonance graphs of benzenoid systems, tubulenes, and fullerenes. We introduce the concept of the generalized Zhang-Zhang polynomial for these molecules. Instead of considering only interactions between 6-cycles (Clar covers), we also consider 10-cycles, which contribute to the resonance energy of a molecule as well. Therefore, we generalize the concepts of the Zhang-Zhang polynomial of the underlying molecular graphs and the cube polynomial of the corresponding resonance graph and prove the equality of these two polynomials.