標題: Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures: Prolate rectangles and their generalizations
作者: Chou, Chien-Pin
Kang, Jin-Su
Witek, Henryk A.
應用化學系
應用化學系分子科學碩博班
經營管理研究所
Department of Applied Chemistry
Institute of Molecular science
Institute of Business and Management
關鍵字: Perfect matching;Clar cover;Clar structure;Zhang-Zhang polynomial
公開日期: 10-Jan-2016
摘要: We show that the Zhang-Zhang (ZZ) polynomial of a benzenoid obtained by fusing a parallelogram M(m, n) with an arbitrary benzenoid structure ABC can be simply computed as a product of the ZZ polynomials of both fragments. It seems possible to extend this important result also to cases where both fused structures are arbitrary Kekulean benzenoids. Formal proofs of explicit forms of the ZZ polynomials for prolate rectangles Pr(m, n) and generalized prolate rectangles Pr ([m(1), m(2), ..., m(n)], n) follow as a straightforward application of the general theory, giving ZZ (Pr (m, n), x) = (1 + (1 x) . m)(n) and ZZ(Pr([m(1), m(2), ..., m(n)), n), x) = Pi(n)(k=1)(1 + (1 + x) . m(k)). (C) 2015 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.dam.2015.06.020
http://hdl.handle.net/11536/129494
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.06.020
期刊: DISCRETE APPLIED MATHEMATICS
Volume: 198
起始頁: 101
結束頁: 108
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