Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures: Prolate rectangles and their generalizations

Chien Pin Chou, Jin Su Kang, Henryk A. Witek

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish
JournalDiscrete Applied Mathematics
DOIs
Publication statusAccepted/In press - 2014 Sep 18
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

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