標題: Connectivity Graphs for Single Zigzag Chains and their Application for Computing ZZ Polynomials
作者: Langner, Johanna
Witek, Henryk A.
應用化學系
應用化學系分子科學碩博班
Department of Applied Chemistry
Institute of Molecular science
關鍵字: benzenoids;Clar cover;interface theory;connectivity graph;Zhang-Zhang polynomial;ZZ polynomial
公開日期: 1-Dec-2017
摘要: 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.
URI: http://dx.doi.org/10.5562/cca3191
http://hdl.handle.net/11536/144491
ISSN: 0011-1643
DOI: 10.5562/cca3191
期刊: CROATICA CHEMICA ACTA
Volume: 90
起始頁: 391
結束頁: 400
Appears in Collections:Articles