Original scientific paper

https://doi.org/10.5562/cca3191

Connectivity Graphs for Single Zigzag Chains and their Application for Computing ZZ Polynomials

Johanna Langner ; Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu, Taiwan
Henryk A. Witek orcid.org/0000-0002-9013-1287 ; Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu, Taiwan

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.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Keywords

benzenoids; Clar cover; interface theory; connectivity graph; Zhang-Zhang polynomial; ZZ polynomial

Hrčak ID:

190440

URI

https://hrcak.srce.hr/190440

Publication date:

18.12.2017.

Visits: 1.524 *