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

Chien Pin Chou*, Henryk A. Witek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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)·m)n and ZZ(Pr([m1,m2,⋯, mn],n),x)=π;k=1 n(1+(1+x )· mk).

Original languageAmerican English
Pages (from-to)101-108
Number of pages8
JournalDiscrete Applied Mathematics
Volume198
DOIs
StatePublished - 10 Jan 2016

Keywords

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

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