A relation between Clar covering polynomial and cube polynomial

Abstract

The Clar covering polynomial (also called Zhang-Zhang polynomial in some chemical literature) of a hexagonal system is a counting polynomial for some types of resonant structures called Clar covers, which can be used to determine Kekul\'e count, the first Herndon number and Clar number, and so on. In this paper we find that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a one-to-one correspondence between the Clar covers of H and the hypercubes in R(H). Accordingly, some applications are presented.