## 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 language | English |
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Article number | 2060 |

Number of pages | 14 |

Journal | Symmetry-Basel |

Volume | 12 |

Issue number | 12 |

DOIs | |

State | Published - 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