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“Crowns”, and aromatic sextets in primitive coronoid hydrocarbons

“Crowns” und aromatische Sextette in einfachen coronoiden Kohlenwasserstoffen

  • Organische Chemie Und Biochemie
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Summary

A type of graphs derived from a cycle and associated with primitive coronoids are referred to as “crowns”. The characteristic polynomials and matching polynomials of crowns are studied. These notions are used to calculate the sextet polynomial for primitive coronoids. Patterns of aromatic sextets are treated in some detail.

Zusammenfassung

Eine Graphentype, die von einem Cyclus abgeleitet ist und mit einfachen Coronoiden verknüpft ist, wird als “Crown” bezeichnet. Die charakteristischen Polynome und die „matching“ Polynome der Crowns werden untersucht. In diesem Rahmen werden die Sextett-Polynome für einfache Coronoide berechnet. Die Muster der aromatischen Sextette werden im Detail behandelt.

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References

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

    Google Scholar 

  2. Cyvin B. N., Cyvin S. J., Brunvoll J. (1988) Monatsh. Chem.119: 563

    Google Scholar 

  3. Cyvin S. J. (1989) Monatsh. Chem.120: 243

    Google Scholar 

  4. Bergan J. L., Cyvin S. J., Cyvin B. N. (1987) Chem. Phys. Letters125: 218

    Google Scholar 

  5. Hosoya H. (1986) Comp. & Maths. with Appls.12B: 271; reprinted in: Symmetry Unifying Human Understanding (Hagittai I., ed.). Pergamon Press, New York

    Google Scholar 

  6. Babić D., Graovac A. (1986) Croat. Chem. Acta59: 731

    Google Scholar 

  7. Bergan J. L., Cyvin B. N., Cyvin S. J. (1987) Acta Chim. Hung.124: 299

    Google Scholar 

  8. Cyvin S. J. (1988) Bull. Chem. Soc. Japan61: 4445

    Google Scholar 

  9. Cyvin S. J. (1988) Chem. Phys. Letters147: 384

    Google Scholar 

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

    Google Scholar 

  11. Staab H. A., Diederich F. (1983) Chem. Ber.116: 3487

    Google Scholar 

  12. Staab H. A., Diederich F., Krieger C., Schweitzer D., Chem. Ber.116: 3504

  13. Staab H. A., Diederich F., Čaplar V. (1983) Liebigs Ann. Chem.: 2262

  14. Staab H. A., Sauer M. (1984) Liebigs Ann. Chem.: 742

  15. Funhoff D. J. H., Staab H. A. (1986) Angew. Chem.98: 757

    Google Scholar 

  16. Gutman I., Trinajstić N. (1975) Croat. Chem. Acta47: 507

    Google Scholar 

  17. Graovac A., Gutman I., Trinajstić N. (1977) Topological Approach to the Chemistry of Conjugated Molecules. Springer, Berlin Heidelberg New York (Lecture Notes in Chemistry, Vol. 4)

    Google Scholar 

  18. Cvetković D., Doob M., Sachs H (1980) Spectra of Graphs—Theory and Application. Academic Press, New York

    Google Scholar 

  19. Trinajstić N. (1983) Chemical Graph Theory, Vols. I–II. CRC Press, Boca Raton, Fl.

    Google Scholar 

  20. Farrell E. J. (1979) Discrete Math.25: 121

    Google Scholar 

  21. Farrell E. J. (1979) J. Comb. Theory27B: 75

    Google Scholar 

  22. Gutman I. (1979) Match (Mülheim)6: 75

    Google Scholar 

  23. Godsil C. D., Gutman I. (1979) Z. Naturforsch.34a: 776

    Google Scholar 

  24. Godsil C. D., Gutman I. (1981) Croat. Chem. Acta54: 53

    Google Scholar 

  25. Godsil C. D., Gutman I. (1981) J. Graph Theory5: 137

    Google Scholar 

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

    Google Scholar 

  27. Harary F., Schwenk A. J. (1973) Discrete Math.6: 359

    Google Scholar 

  28. Gutman I., El-Basil S. (1985) Z. Naturforsch.40a: 923

    Google Scholar 

  29. El-Basil S. (1987) J. Math. Chem.1: 153

    Google Scholar 

  30. El-Basil S. (1986) J. Chem. Soc., Faraday Trans. II82: 299

    Google Scholar 

  31. Cyvin S. J., Gutman I. (1988) Kekulé Structures in Benzenoid Hydrocarbons. Springer, Berlin Heidelberg New York Tokyo (Lecture Notes in Chemistry, Vol. 46)

    Google Scholar 

  32. Hosoya H., Yamaguchi T. (1975) Tetrahedron Letters: 4659

  33. Gutman I., Cyvin S. J. (1989) Bull. Chem. Soc. Japan62: 1250

    Google Scholar 

  34. Ohkami N., Motoyama A., Yamaguchi T., Hosoya H., Gutman I. (1981) Tetrahedron37: 1113

    Google Scholar 

  35. Gutman I., El-Basil S. (1984) Z. Naturforsch.39a: 276

    Google Scholar 

  36. Aihara J. (1976) Bull. Chem. Soc. Japan49: 1429

    Google Scholar 

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Fuji, Z., Cyvin, S.J. & Cyvin, B.N. “Crowns”, and aromatic sextets in primitive coronoid hydrocarbons. Monatsh Chem 121, 421–432 (1990). https://doi.org/10.1007/BF00809459

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  • DOI: https://doi.org/10.1007/BF00809459

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