Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871243 | Discrete Applied Mathematics | 2018 | 7 Pages |
Abstract
This paper offers a formal explanation of a rather puzzling and surprising equivalence between the Clar covering polynomials of single zigzag chains and the tiling polynomials of 2Ãn rectangles for tilings using 1Â ÃÂ 2, 2Â ÃÂ 1 and 2Â ÃÂ 2 tiles. It is demonstrated that the set of Clar covers of single zigzag chains N(nâ1) is isomorphic to the set of tilings of a 2Ãn rectangle. In particular, this isomorphism maps Clar covers of N(nâ1) with k aromatic sextets to tilings of a 2Ãn rectangle using k square 2Â ÃÂ 2 tiles. The proof of this fact is an application of the recently introduced interface theory of Clar covers. The existence of a similar relationship between the Clar covers of more general benzenoid structures and more general tilings of rectangles remains an interesting open problem in chemical graph theory.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Johanna Langner, Henryk A. Witek,