Zhang-Zhang polynomials of regular 3- and 4-tier benzenoid strips

Henryk A. Witek*, Grzegorz Mos̈, Chien Pin Chou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We present compact, closed-form expressions for Zhang-Zhang (ZZ) polynomials of regular 3- and 4-tier benzenoid strips. It is possible to unify the ZZ polynomials of 11 classes of regular 3- and 4-tier benzenoid strips into a single, universal, three-parameter formula (Equation Presented) where Cl ∈ {2,3,4,5,6}, a0 = 1, a1 ∈ {0,1,2,3}, and a2 ∈ {0,1}. The parameters and partition the a1 and a2 tiers benzenoid strips into four superfamilies; a1 and a2 are constant within a given superfamily and enumerates subsequent benzenoid structures. Our finding provides also a compact and universal expression for the number of Kekulé structures for regular 3- and 4-tier benzenoid strips given by (Equation Presented) These expressions are expected to be readily applicable also to wider regular benzenoid strips.

Original languageEnglish
Pages (from-to)427-442
Number of pages16
JournalMatch
Volume73
Issue number2
StatePublished - 1 Jan 2015

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