An Algorithm and FORTRAN Program for Automatic Computation of the Zhang-Zhang Polynomial of Benzenoids

Abstract

"An automatic computer code is developed to calculate the Zhang-Zhang (ZZ) polynomial (aka Clar covering polynomial) for benzenoid systems. The code can be routinely applied to dense pericondensed benzenoids containing up to 500 carbon atoms. For catacondensed and quasi-linear pericondensed benzenoid systems, the limiting number of atoms is much larger and may exceed 10000. A parallel implementation of the code is also presented, which allows one to surpass these limits with a large number of CPUs. The developed program is applied for finding the ZZ polynomials of various classes of benzenoid systems; general techniques and algorithms applicable in this context are reviewed and discussed. A survey of new results obtained in that way is presented in a sequel to this paper [C.-P. Chou, Y. Li, and H.A. Witek, MATCH Commun. Math. Comput. Chem., submitted]."