### Abstract

Closed-form, general formulas for the Zhang-Zhang (ZZ) polynomials for two important classes of benzenoid structures, chevrons Ch(k,m,n) and generalized chevrons Ch(k,m,n1,n2), are formally derived. The derivations rely on a new and important theorem, which states that the ZZ polynomial of two fused parallelograms can be represented as the product of the ZZ polynomials of the two separated fragments. This theoretical result seems to play an important role in the theory of pericondensed benzenoids and may prove useful for the process of discovering closed-form formulas of Zhang-Zhang polynomials of for a wide class of benzenoid structures.

Original language | English |
---|---|

Pages (from-to) | 105-124 |

Number of pages | 20 |

Journal | Match |

Volume | 72 |

Issue number | 1 |

Publication status | Published - 2014 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Chemistry(all)
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Match*,

*72*(1), 105-124.

**Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures : Chevrons and generalized chevrons.** / Chou, Chien Pin; Witek, Henryk A.

Research output: Contribution to journal › Article

*Match*, vol. 72, no. 1, pp. 105-124.

}

TY - JOUR

T1 - Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures

T2 - Chevrons and generalized chevrons

AU - Chou, Chien Pin

AU - Witek, Henryk A.

PY - 2014

Y1 - 2014

N2 - Closed-form, general formulas for the Zhang-Zhang (ZZ) polynomials for two important classes of benzenoid structures, chevrons Ch(k,m,n) and generalized chevrons Ch(k,m,n1,n2), are formally derived. The derivations rely on a new and important theorem, which states that the ZZ polynomial of two fused parallelograms can be represented as the product of the ZZ polynomials of the two separated fragments. This theoretical result seems to play an important role in the theory of pericondensed benzenoids and may prove useful for the process of discovering closed-form formulas of Zhang-Zhang polynomials of for a wide class of benzenoid structures.

AB - Closed-form, general formulas for the Zhang-Zhang (ZZ) polynomials for two important classes of benzenoid structures, chevrons Ch(k,m,n) and generalized chevrons Ch(k,m,n1,n2), are formally derived. The derivations rely on a new and important theorem, which states that the ZZ polynomial of two fused parallelograms can be represented as the product of the ZZ polynomials of the two separated fragments. This theoretical result seems to play an important role in the theory of pericondensed benzenoids and may prove useful for the process of discovering closed-form formulas of Zhang-Zhang polynomials of for a wide class of benzenoid structures.

UR - http://www.scopus.com/inward/record.url?scp=84898712025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898712025&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84898712025

VL - 72

SP - 105

EP - 124

JO - Match

JF - Match

SN - 0340-6253

IS - 1

ER -