  In this paper we study the resonance graphs of benzenoid systems, tubulenes,
and fullerenes. The resonance graph reflects the interactions between the Kekul
e structures of a molecule. The equivalence of the Zhang-Zhang polynomial
(which counts Clar covers) of the molecular graph and the cube polynomial
(which counts hypercubes) of its resonance graph is known for all three
families of molecular graphs.
  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
and the cube polynomial and prove the equality of these two polynomials.
