Abstract
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.
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