ALGORITHM FOR SIMULTANEOUS CALCULATION OF KEKULÉ AND CLAR STRUCTURE COUNTS, AND CLAR NUMBER OF BENZENOID MOLECULES

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.

Keywords:

• Benzenoid hydrocarbons
• Clar number
• Clar structure
• Kekulé
• structure
• sextet polynomial
• Zhang–Zhang polynomial