Zhang–Zhang polynomials of cyclo-polyphenacenes

摘要

The Zhang–Zhang polynomial (i.e., Clar covering polynomial) of hexagonal systems is introduced by H. Zhang and F. Zhang, which can be used to calculate many important invariants such as the Clar number, the number of Kekulé structures and the first Herndon number, etc. In this paper, we give out an explicit recurrence expression for the Zhang–Zhang polynomials of the cyclo-polyphenacenes, and determine their Clar numbers, numbers of Kekulé structures and their first Herndon numbers.