標題: Zhang-Zhang Polynomials of Regular 3-and 4-tier Benzenoid Strips
作者: Witek, Henryk A.
Mos, Grzegorz
Chou, Chien Pin
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
公開日期: 1-Jan-2015
摘要: We present compact, closed-form expressions for Zhang-Zhang (ZZ) polynomials of regular 3- and 4-tier benzenoid strips. It is possible to unify the ZZ polynomials of 11 classes of regular 3- and 4-tier benzenoid strips into a single, universal, three-parameter formula Sigma(Cl)(k=0) Sigma(2)(l=0) a(l) (n +1(k)) (n - l + Cl - k n-1)x(k) where Cl is an element of{2,3,4,5,6}, a(0) = 1, a(1) is an element of{0,1,2,3}, and a(2) is an element of{0,1}. The parameters a(1) and a(2) partition the 3- and 4-tiers benzenoid strips into four superfamilies; a(1) and a(2) are constant within a given superfamily and Cl enumerates subsequent benzenoid structures. Our finding provides also a compact and universal expression for the number of Kekule structures for regular 3- and 4-tier benzenoid strips given by K = Sigma(2)(l=0) a(l)(n - l + Cl Cl) These expressions are expected to be readily applicable also to wider regular benzenoid strips.
URI: http://hdl.handle.net/11536/124735
ISSN: 0340-6253
期刊: MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY
Volume: 73
起始頁: 427
結束頁: 442
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