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Kekulé structure counts for some classes of all-benzenoid and all-coronoid hydrocarbons

Kekulé-Strukturzählungen für einige Klassen von-benzenoiden und all-coronoiden Kohlenwasserstoffen

  • Anorganische Und Physikalische Chemie
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Summary

A general formula for the Kekulé structure count (K) is deduced for the class of catacondensed all-benzenoids with unbranched backbones. The formula is extended to “thin” pericondensed all-benzenoids, where allowance is made for pyrene units. In this treatment the fragmentation matrices are employed. A generalization of these matrices is furnished. Next some generalK formulas for classes of catacondensed and thin pericondensed all-coronoids are deduced. Again the fragmentation matrices are employed, but the problem is also studied in terms of certain polynomials.

Zusammenfassung

Eine generelle Formel für die Kekulé-Strukturzählung (K) für die Klasse der katakondensierten all-Benzenoiden mit unverzweigter Grundstruktur wird abgeleitet. Die Formel wird auf „dünne“ perikondensierte all-Benzenoide ausgeweitet, wobei Pyren-Einheiten mit berücksichtigt werden können. Bei dieser Behandlung werden Fragmentationsmatritzen verwendet und eine Generalisierung dieser Matritzen getroffen. Dann werden einige generelleK-Formeln für Klassen von katakondensierten und dünnen perikondensierten all-coronoiden Verbindungen abgeleitet. Dabei werden wieder Fragmentationsmatritzen angewandt, das Problem wird allerdings auch mit Hilfe bestimmter Polynome untersucht.

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Authors and Affiliations

  1. Division of Physical Chemistry, The University of Trondheim, N-7034, Trondheim-NTH, Norway

    Sven J. Cyvin, Björg N. Cyvin & Jon Brunvoll

  2. Faculty of Science, University of Kragujevac, P.O.Box 60, YU-34000, Kragujevac, Yugoslavia

    Ivan Gutman

Authors
  1. Sven J. Cyvin
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  2. Björg N. Cyvin
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  3. Jon Brunvoll
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  4. Ivan Gutman
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Dedicated to the memory of Professor Oskar E. Polansky, who died in January 1989. He was the one who coined the term “all-benzenoid”.

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Cyvin, S.J., Cyvin, B.N., Brunvoll, J. et al. Kekulé structure counts for some classes of all-benzenoid and all-coronoid hydrocarbons. Monatsh Chem 122, 771–787 (1991). https://doi.org/10.1007/BF00815917

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  • DOI: https://doi.org/10.1007/BF00815917

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