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Number of Kekulé structures of hexagon-shaped benzenoids

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Abstract

An explicit combinatorial formula for the number of Kekulé structures of a hexagon-shaped benzencid system is deduced. Thus, the validity of the previously proposed, but hitherto unproved formulas of Everett (from 195'1), Woodger (from 1951), and Cyvin from 1986) is confirmed. The proof is based on the application of the John-Sachs theorem.

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References

  1. A Gordon and W.H.T. Davison, J. Chem Phys. 20 (1952)428.

    Google Scholar 

  2. T.F. Yen, Theor. Chin. Acta 20 (1971)399.

    Google Scholar 

  3. S.J. Cyvin, Monatsh. Chem. 117 (1986)33.

    Google Scholar 

  4. S.J. Cyvin and I. Gutman,Kekulé Structures in Benzenoid Hydrocarbons, Lecture Notes in Chemistry 46 (Springer-Verlag, Berlin, 1988).

    Google Scholar 

  5. I. Gutman, Z. Naturforsch. 36a (1981)128.

    Google Scholar 

  6. I. Gutman, Bull. Soc. Chin. Beograd 47 (1982)453.

    Google Scholar 

  7. N. Ohkami and H. Hosoya, Theor. Chim. Acta 64 (1983)153.

    Google Scholar 

  8. N. Trinaistić,Chemical Graph Theory, Vol. II (CRC Press, Bora Raton, FL, 1983).

    Google Scholar 

  9. S.J. Cyvin, B.N. Cyvin and I. Gutman, A Naturforsch. 40a (1985)1253.

    Google Scholar 

  10. S.J. Cyvin, B.N. Cyvin and I. Gutman, Coll. Sci. Papers Fac. Sci. Kragujevac 7 (1986)5.

    Google Scholar 

  11. H. Hosoya, Comp. & Maths. with Appls. 12B (1986)271.

    Google Scholar 

  12. I. Gutman and S.J. Cyvin, Chem. Phys. Lett. 136 (1987)137.

    Google Scholar 

  13. K John and H. Sacks, in:Graphen in Forschung and Unterricht, ed. R. Bodendiek, H. Schumacher and H. Walter (Verlag Barbara Franzbecker, Bad Salzdetfurth, FRG, 1985) pp. 85 -101.

    Google Scholar 

  14. I. Gutman, LX Su and S.J. Cyvin, J. Serb. Chem. Soc. 52 (1987)263.

    Google Scholar 

  15. S.J. Cyvin and I. Gutman, J. Mol. Struct, (Theochem) 164 (1988)183.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Science, University of Novi Sad, YU-21 000, Novi Sad, Yugoslavia

    O. Bodroža & R. Tošić

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

    I. Gutman

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

    S. J. Cyvin

Authors
  1. O. Bodroža
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  2. I. Gutman
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  3. S. J. Cyvin
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  4. R. Tošić
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Bodroža, O., Gutman, I., Cyvin, S.J. et al. Number of Kekulé structures of hexagon-shaped benzenoids. J Math Chem 2, 287–298 (1988). https://doi.org/10.1007/BF01167208

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  • DOI: https://doi.org/10.1007/BF01167208

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