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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. March 2006, Volume 5, Number 3, 144-149 |
Kekulé Structure Counts in Damaged Benzenoid Parallelograms
István Lukovits, Ante Milicevic, Nenad Trinajstic, and Damir Vukicevic
Internet Electron. J. Mol. Des. 2006, 5, 144-149
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Abstract:
This report was motivated by a recent paper (T. Doslic,
Perfect Matchings in Lattice Animals and Lattice Paths with
Constraints, Croat. Chem. Acta 2005, 78, 251-259), and an
idea of expressing the number of Kekulé structures of
damaged benzenoid parallelograms by a two-parameter
formula, the parameters being the width and length of the
parallelogram. The number of Kekulé structures appears to
be an important quantity for predicting the stability of
benzenoid structures. All formulas were derived by using the
combinatorial enumeration based on the binomial
coefficients. Formulas for the Kekulé-structure counts of
damaged benzenoid parallelograms are derived. Perimeter-edges
are indicated whose removal produces the least or the
most damaged benzenoid parallelograms. The number of
Kekulé structures of damaged benzenoid parallelograms is
expressible in terms of the width and length of parent structures.
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