Zhang-Zhang Polynomials of Ribbons

Bing-Hau He, Chien-Pin Chou, Johanna Langner, Henryk A. Witek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We report a closed-form formula for the Zhang-Zhang polynomial (also known as ZZ polynomial or Clar covering polynomial) of an important class of elementary peri-condensed benzenoids Rb (n(1), n(2), m(1), m(2)), usually referred to as ribbons. A straightforward derivation is based on the recently developed interface theory of benzenoids [Langner and Witek, MATCH Commun. Math. Comput. Chem. 2020, 84, 143-176]. The discovered formula provides compact expressions for various topological invariants of Rb (n(1), n(2), m(1), m(2)): the number of Kekule structures, the number of Clar covers, its Clar number, and the number of Clar structures. The last two classes of elementary benzenoids, for which closed-form ZZ polynomial formulas remain to be found, are hexagonal flakes O (k, m, n) and oblate rectangles Or (m, n).

Original languageEnglish
Article number2060
Number of pages14
JournalSymmetry-Basel
Volume12
Issue number12
DOIs
StatePublished - Dec 2020

Keywords

  • enumeration of Clar covers
  • ZZ polynomials
  • Clar covering polynomials
  • ribbons
  • peri-condensed benzenoids
  • CLOSED-FORM FORMULAS
  • HEXAGONAL SYSTEMS
  • KEKULE STRUCTURES
  • INTERFACE THEORY
  • ALGORITHM
  • BENZENOIDS
  • NUMBER

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