### Abstract

We show that the Zhang-Zhang (ZZ) polynomial of a benzenoid obtained by fusing a parallelogram M(m,n) with an arbitrary benzenoid structure ABC can be simply computed as a product of the ZZ polynomials of both fragments. It seems possible to extend this important result also to cases where both fused structures are arbitrary Kekuléan benzenoids. Formal proofs of explicit forms of the ZZ polynomials for prolate rectangles Pr(m,n) and generalized prolate rectangles Pr([m1,m2,. .,mn],n) follow as a straightforward application of the general theory, giving ZZ(Pr(m,n),x)=(1+(1+x){dot operator}m)n and ZZ(Pr([m1,m2,. .,mn],n),x)=∏k=1n(1+(1+x){dot operator}mk).

Original language | English |
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Journal | Discrete Applied Mathematics |

DOIs | |

Publication status | Accepted/In press - 2014 Sep 18 |

Externally published | Yes |

### Keywords

- Clar cover
- Clar structure
- Perfect matching
- Zhang-Zhang polynomial

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures: Prolate rectangles and their generalizations'. Together they form a unique fingerprint.

## Cite this

*Discrete Applied Mathematics*. https://doi.org/10.1016/j.dam.2015.06.020