Abstract
The Chinese mathematicians Heping Zhang and Fuji Zhang conceived a combinatorial polynomial associated with benzenoid molecules. This “Zhang–Zhang polynomial” contains information on the Kekulé structure count (K), Clar structure count (C), Clar number (Cl), Hosoya-Yamaguchi sextet polynomial σ(B, x), and several other important characteristics of the underlying benzenoid molecule. We show how one can easily calculate the Zhang-Zhang polynomial, and thus arrive at an algorithm for simultaneous computation of K, C, Cl, and σ(B, x). Some applications of this algorithm are pointed out.
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