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The simplest coronoids: Hollow hexagons

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Abstract

Hollow hexagons form a subclass of primitive coronoid systems. The macrocyclic aromatic hydrocarbon kekulene corresponds to a hollow hexagon. The hollow hexagons for given numbers of hexagonal units (h) were enumerated by computer aid, but also an analytical solution for the numbers of hollow hexagons was achieved. For the Kekulé structure counts (k) of a hollow hexagon a general formula is reported. Also the maximum and minimumK numbers are considered.

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References

  1. Brunvoll, J.; Cyvin, B. N.; Cyvin, S. J.J. Chem. Inf. Comput. Sci.,1987,27, 14.

    Google Scholar 

  2. Balaban, A. T.; Harary, F.Tetrahedron,1968,24, 2505.

    Google Scholar 

  3. Gutman, I.Bull. Soc. Chim. Beograd,1982,47, 453.

    Google Scholar 

  4. Cyvin, S. J.; Gutman, I.Comp. Math. Appls. 1986,12B, 859; reprinted in:SYMMETRY: Unifying Human Understanding; Hargittai, I., Ed.; Pergamon Press, New York, 1986, p. 859.

    Google Scholar 

  5. Gutman, I.; Polansky, O. E.Mathematical Concepts in Organic Chemistry; Springer-Verlag, Berlin, 1986.

    Google Scholar 

  6. Gutman, I.; Cyvin, S. J.Introduction to the Theory of Benzenoid Hydrocarbons; Springer-Verlag, Berlin, 1989.

    Google Scholar 

  7. Jenny, W.; Peter, R.Angew. Chem.,1965,77, 44.

    Google Scholar 

  8. Polansky, O. E.; Rouvray, D. H.Math. Chem. (Mülheim/Ruhr),1977,3, 97.

    Google Scholar 

  9. Dopper, J. E.; Wynberg, H.Tetrahedron Lett.,1972, 763.

  10. Dias, J. R.J. Chem. Inf. Comput. Sci.,1982,22, 15.

    Google Scholar 

  11. Knop, J. V.; Szymanski, K.; Jeričević, Z.; Trinajstić, N.Math. Chem. (Mülheim/Ruhr),1984,16, 119.

    Google Scholar 

  12. Balaban, A. T.Pure Appl. Chem.,1982,54, 1075.

    Google Scholar 

  13. Hall, G. G.Theor. Chim. Acta,1988,73, 425.

    Google Scholar 

  14. Staab, H. A.; Diederich, F.Chem. Ber.,1983,116, 3487.

    Google Scholar 

  15. Staab, H. A.; Diederich, F.; Krieger, C.; Schweitzer, D.Chem. Ber.,1983,116, 3504.

    Google Scholar 

  16. Staab, H. A.; Diederich, F.; Čaplar, V.Liebigs Ann. Chem.,1983, 2262.

  17. Staab, H. A.; Sauer, M.Liebigs Ann. Chem.,1984, 742.

  18. Diederich, F.; Staab, H. A.Angew. Chem. Int. Ed. Engl,1978,17, 372.

    Google Scholar 

  19. Funhoff, D. J. H.; Staab, H. A.Angew. Chem. Int. Ed. Engl.,1986,25, 742.

    Google Scholar 

  20. Balaban, A. T.; Brunvoll, J.; Cioslowski, J.; Cyvin, B. N.; Cyvin, S. J.; Gutman, I.; He, W. C.; He, W. J.; Knop, J. V.; Kovačević, M.; Müller, W. R.; Szymanski, K.; Tošić, R.; Trinajstić, N.Z. Naturforsch., Teil A1987,42, 863.

    Google Scholar 

  21. Harary, F. InGraph Theory and Theoretical Physics; Harary, F. Ed.; Academic Press, London,1967, p. 1.

    Google Scholar 

  22. Harary, F.; Schwenk, A. J.Discrete Mathematics 1973,6, 359.

    Google Scholar 

  23. Cyvin, S. J.; Gutman, I.Kekulé Structures in Benzenoid Hydrocarbons, Springer-Verlag, Berlin,1988.

    Google Scholar 

  24. Bergan, J. L.; Cyvin, S. J.; Cyvin, B. N.Chem. Phys. Lett.,1986,125, 218.

    Google Scholar 

  25. Hosoya, H.Comp. Maths. Appls. 1986,12B, 271; reprinted inSYMMETRY: Unifying Human Understanding; Hargittai, I. Ed.; Pergamon Press, New York, 1986, p. 271.

    Google Scholar 

  26. Babić, D.; Graovac, A.Croat. Chem. Acta,1986,59, 731.

    Google Scholar 

  27. Bergan, J. L.; Cyvin, B. N.; Cyvin, S. J.Acta Chim. Hung.,1987,124, 299.

    Google Scholar 

  28. Cyvin, S. J.; Bergan, J. L.; Cyvin, B. N.Acta Chim. Hung.,1987,124, 691.

    Google Scholar 

  29. Cyvin, S. J.; Cyvin, B. N.; Brunvoll, J.Chem. Phys. Lett.,1987,140, 124.

    Google Scholar 

  30. Cyvin, S. J.; Cyvin, B. N.; Brunvoll, J.; Bergan, J. L.Coll. Sci. Papers Fac. Sci. Kragujevac,1987,8, 137.

    Google Scholar 

  31. Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Acta Chem. Scand.,1988.A42, 434.

    Google Scholar 

  32. Cyvin, S. J.Chem. Phys. Lett.,1988,147, 384.

    Google Scholar 

  33. Cyvin, B. N.; Cyvin, S. J.; Brunvoll, J.Monatsh. Chem.,1988,119, 563.

    Google Scholar 

  34. Cyvin, S. J.Bull. Chem. Soc. Jpn.,1988,61, 4445.

    Google Scholar 

  35. Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Comp. Math. Appls.,1989,17, 355; reprinted in:SYMMETRY 2: Unifying Human Understanding; Hargittai, I. Ed.; Pergamon Press, New York,1989, p. 355.

    Google Scholar 

  36. Brunvoll, J.; Cyvin, S. J.; Cyvin, B. N.; Gutman, I.; Tošić, R.; Kovačević, M.J. Mol. Struct. (Theochem.),1989,184, 165.

    Google Scholar 

  37. Cyvin, S. J.Monatsh. Chem.,1989,120, 243.

    Google Scholar 

  38. Knop, J. V.; Müller, W. R.; Szymanski, K.; Trinajstić, N.Math. Chem. (Mülheim/Ruhr),1986,20, 197.

    Google Scholar 

  39. He, W. J.; He, W. C.; Wang, Q. X.; Brunvoll, J.; Cyvin, S. J.Z. Naturforsch., Teil A,1988,43, 693.

    Google Scholar 

  40. Brunvoll, J.; Cyvin, B. N.; Cyvin, S. J.J. Chem. Inf. Comput. Sci.,1987,27, 171.

    Google Scholar 

  41. Yamamoto, K.; Harada, T.; Nakazaki, M.; Naka, T.; Kai, Y.; Harada, S.; Kasai, N.J. Am. Chem. Soc.,1983,105, 7171.

    Google Scholar 

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Authors and Affiliations

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

    Sven J. Cyvin, Jon Brunvoll, Björg N. Cyvin, John L. Bergan & E. Brendsdal

Authors
  1. Sven J. Cyvin
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  2. Jon Brunvoll
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  3. Björg N. Cyvin
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  4. John L. Bergan
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  5. E. Brendsdal
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Additional information

This article is Part VI of the series “Enumeration and Classification of Coronoid Hydrocarbons.” For Part V, see ref. [36].

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Cyvin, S.J., Brunvoll, J., Cyvin, B.N. et al. The simplest coronoids: Hollow hexagons. Struct Chem 2, 555–566 (1991). https://doi.org/10.1007/BF00673438

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  • DOI: https://doi.org/10.1007/BF00673438

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