Advertisement

Structural Chemistry

, Volume 7, Issue 4, pp 263–271 | Cite as

Theory of helicenic hydrocarbons. Part 5: Irreducible helicenes and their enumeration

  • Zhang Fuji
  • J. Brunvoll
  • S. J. Cyvin
  • B. N. Cyvin
  • Guo Xiaofeng
  • A. A. Dobrynin
Article

Abstract

An irreducible helicene is a helicene from which no hexagon can be deleted if it shall remain to be a helicene. The generation of irreducible helicenes from primitive coronoids is treated, and algebraic expressions are deduced for their numbers. Symmetry plays an important role in this treatment. Numerical results obtained with the aid of computer programming are reported.

Key words

Primitive coronoid irreducible helicene enumeration 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cyvin, S. J.; Zhang, F. J.; Cyvin, B. N.; Guo, X. F.Struct. Chem. 1993,4, 149.Google Scholar
  2. 2.
    Trinajstić, N.Chemical Graph Theory, 2nd ed.; CRC Press: Boca Raton, 1983.Google Scholar
  3. 3.
    Cyvin, S. J.; Gutman, I.Kekulé Structures in Benzenoid Hydrocarbons (Lecture Notes in Chemistry, Vol. 46); Springer-Verlag: Berlin, 1988.Google Scholar
  4. 4.
    Gutman, I.; Cyvin, S. J.Introduction to the Theory of Benzenoid Hydrocarbons; Springer-Verlag: Berlin, 1989.Google Scholar
  5. 5.
    Cyvin, B. N.; Brunvoll, J.; Cyvin, S. J. InAdvances in the Theory of Benzenoid Hydrocarbons, Vol. II; Gutman, I., Ed.;Topics in Current Chemistry, Vol. 162; Springer-Verlag: Berlin, 1992; p. 65.Google Scholar
  6. 6.
    Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Theory of Coronoid Hydrocarbons (Lecture Notes in Chemistry, Vol. 54); Springer-Verlag: Berlin. 1991.Google Scholar
  7. 7.
    Brunvoll, J.; Cyvin, B. N.; Cyvin, S. J.J. Chem. Inf. Comput. Sci. 1987,27, 14.Google Scholar
  8. 8.
    Brunvoll, J.; Cyvin, B. N.; Cyvin, S. J.; Gutman, I.; Tošić, R.; Kovačević, M.J. Mol. Struct. (Theochem)1989,184, 165.Google Scholar
  9. 9.
    Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Struct. Chem. 1990,1, 429.Google Scholar
  10. 10.
    Cyvin, S. J.; Cyvin, B. N.; Brunvoll, J.Struct. Chem. 1994,5, 295Google Scholar
  11. 11.
    Brunvoll, J.; Cyvin, S.J.; Cyvin, B. N.; Zhang, F. J.; Guo, X. F.Struct. Chem. 1996,7, 119.Google Scholar
  12. 12.
    Guo, X. F.; Zhang, F.J.; Cyvin, S. J.; Cyvin, B. N.Polycyclic Aromatic Compounds 1993,3, 261.Google Scholar
  13. 13.
    Zhang, F. J.; Guo, X. F.; Cyvin, S. J.; Cyvin, B. N.Polycyclic Aromatic Compounds 1994,4, 115.Google Scholar
  14. 14.
    Dobrynin, A. A. Vychislitelnye Sistemy (in Russian)1990,136, 16.Google Scholar
  15. 15.
    Harary, F.; Palmer, E. M.Graphical Enumerations; Academic Press: New York, 1973.Google Scholar
  16. 16.
    Cyvin, S. J.; Brunvoll, J.; Cyvin, B. N.Acta Chem. Scand. 1988,A42, 434.Google Scholar
  17. 17.
    Brunvoll, J.; Cyvin, S. J.; Cyvin, B. N.J. Comput. Chem. 1987,8, 189.Google Scholar
  18. 18.
    Brunvoll, J.; Cyvin, B. N.; Cyvin, S. J.J. Chem. Inf. Comput. Sci. 1987,27, 171.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Zhang Fuji
    • 1
  • J. Brunvoll
    • 2
  • S. J. Cyvin
    • 2
  • B. N. Cyvin
    • 2
  • Guo Xiaofeng
    • 3
  • A. A. Dobrynin
    • 4
  1. 1.Department of MathematicsXiamen UniversityFujianP.R. China
  2. 2.Department of Physical ChemistryThe University of TrondheimTrondheim-NTHNorway
  3. 3.Department of MathematicsXinjiang UniversityWulumuqiP.R. China
  4. 4.Siberian Branch of Russian Academy of SciencesInstitute of MathematicsNovosibirskRussia

Personalised recommendations