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Zhang–Zhang polynomials of cyclo-polyphenacenes

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Abstract

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.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, 410081, People’s Republic of China

    Qiuzhi Guo, Hanyuan Deng & Dandan Chen

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  1. Qiuzhi Guo
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  2. Hanyuan Deng
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  3. Dandan Chen
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Correspondence to Hanyuan Deng.

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Guo, Q., Deng, H. & Chen, D. Zhang–Zhang polynomials of cyclo-polyphenacenes. J Math Chem 46, 347–362 (2009). https://doi.org/10.1007/s10910-008-9466-4

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