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. The resonance graph reflects the interactions between the Kekule 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 ZhangZhang polynomial and the cube polynomial and prove the equality of these two polynomials. Mathematics Subject Classification (2010) Primary 05C31; Secondary 92E10.