Connectivity graphs for single zigzag chains and their application for computing ZZ polynomials

Johanna Langner, Henryk A. Witek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We present a graph-theoretical interpretation of the recently developed interface theory of single zigzag chains N(n) in form of connectivity graphs. A remarkable property of the connectivity graphs is the possibility of constructing the full set of Clar covers of N(n) as the complete set of walks on these graphs. Connectivity graphs can be constructed in a direct form, in which the number of vertices is growing linearly with the length n of N(n), and in a reduced form, in which the number of vertices is independent of the actual length of the chain. The presented results can be immediately used for the determination of the Zhang-Zhang (ZZ) polynomials of N(n) in an easy and natural manner. Two techniques for computing the ZZ polynomial are proposed, one based on direct recursive computations and the other based on a general solution to a set of recurrence relations. Generalization of the interface theory to arbitrary benzenoid structures, the construction of associated connectivity graphs, and techniques for the computation of the associated ZZ polynomials will be presented in the near future.

Original languageEnglish
Pages (from-to)391-400
Number of pages10
JournalCroatica Chemica Acta
Volume90
Issue number3
DOIs
StatePublished - Jun 2017

Keywords

  • Benzenoids
  • Clar cover
  • Connectivity graph
  • Interface theory
  • Zhang-Zhang polynomial
  • ZZ polynomial

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