TY - JOUR
T1 - Enumeration of Clar covers of parallelogram chains
AU - He, Bing Hau
AU - Witek, Henryk A.
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/10/30
Y1 - 2021/10/30
N2 - The number of Clar covers, the number of Kekulé structures, and the Clar covering polynomials (aka Zhang–Zhang or ZZ polynomials) of benzenoid parallelogram chains Mkm,n formed by merging k benzenoid parallelograms Mm,n are characterized in terms of analogous quantities of the elementary building block, Mm,n. The appropriate formulas are compactly expressed as determinants of highly structured, tridiagonal, Toeplitz k×k matrices. All the 2k distinct parallelogram chains Mkm,n≡M1M2…Mk of constant length k, where Mi∈R≡Mm,n,L≡Mn,m, share the same ZZ polynomial and consequently possess the same number of Clar covers and Kekulé structures. The presented results constitute the first attempt to express the Clar theory of complex benzenoid moieties in terms of elementary benzenoids.
AB - The number of Clar covers, the number of Kekulé structures, and the Clar covering polynomials (aka Zhang–Zhang or ZZ polynomials) of benzenoid parallelogram chains Mkm,n formed by merging k benzenoid parallelograms Mm,n are characterized in terms of analogous quantities of the elementary building block, Mm,n. The appropriate formulas are compactly expressed as determinants of highly structured, tridiagonal, Toeplitz k×k matrices. All the 2k distinct parallelogram chains Mkm,n≡M1M2…Mk of constant length k, where Mi∈R≡Mm,n,L≡Mn,m, share the same ZZ polynomial and consequently possess the same number of Clar covers and Kekulé structures. The presented results constitute the first attempt to express the Clar theory of complex benzenoid moieties in terms of elementary benzenoids.
KW - Benzenoid
KW - Clar cover
KW - Kekulé structure
KW - Zhang–Zhang polynomial
UR - http://www.scopus.com/inward/record.url?scp=85093658792&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2021.07.003
DO - 10.1016/j.dam.2021.07.003
M3 - Article
AN - SCOPUS:85093658792
SN - 0166-218X
VL - 302
SP - 221
EP - 233
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -