Skip to main content
Log in

Algebraic structure count of cyclobutadieno-annelated unbranched phenylenes

Algebraische Strukturzählung von cyclobutadieno-annelierten unverzweigten Phenylenen

  • Anorganische Und Physikalische Chemie
  • Published:
Monatshefte für Chemie / Chemical Monthly Aims and scope Submit manuscript

Summary

The calculation of the algebraic structure count of a cyclobutadieno-annelated unbranched phenylene is reduced to an enumeration of the Kekulé structures of an unbranched catacondensed benzenoid system. For the latter computation, easy and well-known algorithms exist.

Zusammenfassung

Die Berechnung des algebraischen Strukturzählers eines unverzweigten cyclobutadieno-annelierten Phenylens wird auf die numerische Ermittlung der Kekulé-Strukturen eines unverzweigten cactakondensierten benzenoiden Systems zurückgeführt. Für letztere stehen einfache und bekannte Algorithmen zur Verfügung.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Clar E., Kemp W., Stewart D. G. (1958) Tetrahedron3: 325

    Google Scholar 

  2. Carter P. G. (1949) Trans. Faraday. Soc.45: 597

    Google Scholar 

  3. Gutman I., Trinajstić N., Wilcox C. F. (1975) Tetrahedron31: 143

    Google Scholar 

  4. Swinborne-Sheldrake R., Herndon W. C., Gutman I. (1975) Tetrahedron Lett.: 755

  5. Hall G. G. (1981) Bull. Inst. Math. Appl.17: 70

    Google Scholar 

  6. Hall G. G. (1991) Int. J. Quant. Chem.39: 605

    Google Scholar 

  7. Dewar M. J. S., Longuet-Higgins H. C. (1952) Proc. Roy. Soc. (London)A214: 482

    Google Scholar 

  8. Wilcox C. F. (1968) Tetrahedron Lett.: 795

  9. Wilcox C. F. (1969) J. Am. Chem. Soc.91: 2732

    Google Scholar 

  10. Herndon W. C. (1973) Tetrahedron29: 3

    Google Scholar 

  11. Herndon W. C. (1974) J. Chem. Educ.51: 10

    Google Scholar 

  12. Graovac A., Gutman I., Trinajstić N. (1977) Topological Approach to the Chemistry of Conjugated Molecules. Springer, Berlin Heidelberg New York

    Google Scholar 

  13. Trinajstić N. (1992) Chemical Graph Theory, 2nd edn. CRC Press, Boca Raton, Fl, chapters 8 and 9

    Google Scholar 

  14. Wilcox C. F., Gutman I., Trinajstić N. (1975) Tetrahedron31: 147

    Google Scholar 

  15. Toda F., Garratt, P. (1992) Chem. Rev.92: 1685

    Google Scholar 

  16. Cyvin S. J., Cyvin B. N., Brunvoll J., Hosoya H., Zhang F., Klein D. J., Chen R., Polansky O. E. (1991) Monatsh. Chem.122: 435

    Google Scholar 

  17. Narumi H., Hosoya H., Murakami H. (1991) J. Math. Phys.32: 1885

    Google Scholar 

  18. Hosoya H., Harary, F. (1993) J. Math. Chem.12: 211

    Google Scholar 

  19. Hosoya H. (1971) Bull. Chem. Soc. Jap.44: 2332

    Google Scholar 

  20. Cyvin S. J., Gutman I. (1988) Kekulé Structures in Benzenoid Hydrocarbons. Springer, Berlin Heidelberg New York Tokyo

    Google Scholar 

  21. Gutman I. (1984) Z. Naturforsch.39A: 794

    Google Scholar 

  22. Gutman I. (1993) Indian J. Chem. A32: 281

    Google Scholar 

  23. Gutman I. (1976) Croat. Chem. Acta48: 289

    Google Scholar 

  24. Klein D. J., Schmalz T. G., El-Basil E., Randić M., Trinajstić N. (1988) J. Mol. Struct. (Theochem.)179: 99

    Google Scholar 

  25. Randić M., Plavšić D., Trinajstić N. (1991) Polycyc. Arom. Comp.2: 183

    Google Scholar 

  26. Gutman I., Cyvin S. J. (1989) Introduction to the Theory of Benzenoid Hydrocarbons. Springer, Berlin, Heidelberg New York Tokyo, pp 112–114

    Google Scholar 

  27. Gutman I. (1993) J. Chem. Soc., Faraday Trans.89: 2413

    Google Scholar 

  28. Gutman I. (1977) Theor. Chim. Acta45: 309

    Google Scholar 

  29. Gordon M., Davison W. H. T. (1952). J. Chem. Phys.20: 428

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gutman, I., Kirby, E.C. Algebraic structure count of cyclobutadieno-annelated unbranched phenylenes. Monatsh Chem 125, 539–547 (1994). https://doi.org/10.1007/BF00811846

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00811846

Keywords

Navigation