کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6871243 | 1440180 | 2018 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Equivalence between Clar covering polynomials of single zigzag chains and tiling polynomials of 2Ãn rectangles
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 243, 10 July 2018, Pages 297-303
Journal: Discrete Applied Mathematics - Volume 243, 10 July 2018, Pages 297-303
نویسندگان
Johanna Langner, Henryk A. Witek,