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Theory of helicenic hydrocarbons. Part 1: Invariants and symmetry

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Abstract

Helicenes form a subclass of polyhexes and correspond to hydrocarbons of considerable chemical interest. This paper is the first part of a general graph-theoretical treatment of helicenes. The invariants are studied: the relations between them, their possible values, and their upper and lower bounds in helicenes. Extremal helicenes and circular helicenes are useful definitions of subclasses of the systems under consideration. Finally an account of symmetry of helicenes is given.

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References

  1. Trinajistić, N.Chemical Graph Theory; CRC Press: Boca Raton, FL, 1983; Vols. I, II.

    Google Scholar 

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

    Google Scholar 

  3. Dias, J. R.Handbook of Polycyclic Hydrocarbons, Part A:Benzenoid Hydrocarbons; Elsevier: Amsterdam, 1987.

    Google Scholar 

  4. Cyvin, S. J.; Gutman, I.Kekulé Structures in Benzenoid Hydrocarbons; Lecture Notes in Chemistry, Vol. 46; Springer-Verlag: Berlin, 1988.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  7. Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Struct. Chem. 1990,1, 429.

    Google Scholar 

  8. Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Theory of Coronoid Hydrocarbons; Lecture Notes in Chemistry, Vol. 54; Springer-Verlag: Berlin, 1991.

    Google Scholar 

  9. Bonchev, D.; Balaban, A. T.J. Chem. Inf. Comput. Sci. 1981,21, 223.

    Google Scholar 

  10. Cyvin, B. N.; Brunvoll, J.; Cyvin, S. J. InAdvances in the Theory of Benzenoid Hydrocarbons; Gutman, I. Ed.; Springer-Verlag: Berlin,1992; p. 65. Vol. II.

    Google Scholar 

  11. Smith, F. T.J. Chem. Phys. 1961,34, 793.

    Google Scholar 

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

    Google Scholar 

  13. Nikolić, S.; Trinajstić, N.; Knop, J. V.; Müller, W. R.; Szymanski, K.J. Math. Chem. 1990,4, 357.

    Google Scholar 

  14. Newman, M. S.; Lutz, W. B.; Lednicer, D.J. Am. Chem. Soc. 1955,77, 3420.

    Google Scholar 

  15. Newman, M. S.; Lednicer, D.J. Am. Chem. Soc. 1956,78, 4765.

    Google Scholar 

  16. Martin, R. H.Angew. Chem. Int. Ed. Engl. 1974,13, 649.

    Google Scholar 

  17. van den Hark, T. E. M.; Noordic, J. H.; Beurskens, P. T.Cryst. Struct. Comm. 1974,3, 443.

    Google Scholar 

  18. Laarhoven, W. H.; Nivard, R. J. F.Tetrahedron 1976,32, 2445.

    Google Scholar 

  19. Clar, E.The Aromatic Sextet; Wiley: London, 1972.

    Google Scholar 

  20. Randić, M.; Gimarc, B. M.; Nikolić, S.; Trinajstić, N.Gazetta Chim. Ital. 1989,119, 1.

    Google Scholar 

  21. Randić, M.; Nikolić, S.; Trinajstić, N.Croat. Chem. Acta 1988,61, 821.

    Google Scholar 

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

    Google Scholar 

  23. Brunvoll, J.; Cyvin, S. J.Z. Naturforsch. 1990,45a, 69.

    Google Scholar 

  24. Polansky, O. E.; Rouvray, D. H.Math. Chem. (Mülheim/Ruhr) 1976,2, 63.

    Google Scholar 

  25. Harary, F.; Harborth, H.J. Combin. Inf. System Sci. 1976,1, 1.

    Google Scholar 

  26. Cyvin, S. J.; Brunvoll, J.Chem. Phys. Lett. 1991,776, 413.

    Google Scholar 

  27. Cyvin, S. J.Theor. Chim. Acta,1992,81, 269.

    Google Scholar 

  28. Brunvoll, J.; Cyvin, B. N.; Cyvin, S. J. InAdvances in the Theory of Benzenoid Hydrocarbons, Gutman, I. Ed.; Springer-Verlag: Berlin,1992; p. 181. Vol. II.

    Google Scholar 

  29. Brunvoll, J.; Cyvin, B. N.; Cyvin, S.J. J. Math. Chem., in press.

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

    Google Scholar 

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

    Google Scholar 

  32. Balaban, A. T.Tetrahedron 1971,27, 6115.

    Google Scholar 

  33. Cyvin, S. J.; Brunvoll, J.; Gutman, I.Rev. Roumaine Chim. 1990,35, 996.

    Google Scholar 

  34. Dias, J. R.J. Chem. Inf. Comput. Sci. 1990,30, 61.

    Google Scholar 

  35. Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Math. Chem. (Mülheim/Ruhr) 1991,26, 27.

    Google Scholar 

  36. Dias, J. R.J. Chem. Inf. Comput. Sci. 1990,30, 251.

    Google Scholar 

  37. Dias, J. R.Theor. Chim. Acta 1990,77, 143.

    Google Scholar 

  38. Dias, J. R.Z. Naturforsch. 1990,45a, 1335.

    Google Scholar 

  39. Dias, J. R.Chem. Phys. Lett. 1991,176, 559.

    Google Scholar 

  40. Dias, J. R.Theor. Chim. Acta 1991,81, 125.

    Google Scholar 

  41. Cyvin, S. J.; Gutman, I.Comput. Math. Appl. 1986,12B, 859; reprinted inSymmetry Unifying Human Understanding; Hargittai, I. Ed.; Pergamon Press: New York, 1986.

    Google Scholar 

  42. Balaban, A. T.Tetrahedron 1969,25, 2949.

    Google Scholar 

  43. Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.J. Math. Chem. 1992,9, 19.

    Google Scholar 

  44. Cyvin, S. J.; Brunvoll, J.J. Math. Chem. 1992,9, 33.

    Google Scholar 

  45. Cyvin, S. J.; Cyvin, B. N.; Brunvoll, J.Math. Chem. (Mülheim/Ruhr) 1991,26, 63.

    Google Scholar 

  46. He, W. C.; He, W. J.Tetrahedron 1986,42, 5291.

    Google Scholar 

  47. Cyvin, S. J.; Brunvoll, J.Polycyclic Aromatic Compounds 1991,2, 209.

    Google Scholar 

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Authors and Affiliations

  1. Division of Physical Chemistry, University of Trondheim, Trondheim, Norway

    S. J. Cyvin & B. N. Cyvin

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  1. S. J. Cyvin
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  2. Zhang Fuji
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  3. B. N. Cyvin
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  4. Guo Xiaofeng
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On leave from: Department of Mathematics, Xinjiang University, Wulumuqi Xinjiang 830046, People's Republic of China.

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Cyvin, S.J., Fuji, Z., Cyvin, B.N. et al. Theory of helicenic hydrocarbons. Part 1: Invariants and symmetry. Struct Chem 4, 149–160 (1993). https://doi.org/10.1007/BF00679341

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  • DOI: https://doi.org/10.1007/BF00679341

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