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
Brunvoll J., Cyvin B. N., Cyvin S. J. (1987) J. Chem. Inf. Comput. Sci.27: 14
Cyvin B. N., Cyvin S. J., Brunvoll J. (1988) Monatsh. Chem.119: 563
Cyvin S. J. (1989) Monatsh. Chem.120: 243
Bergan J. L., Cyvin S. J., Cyvin B. N. (1987) Chem. Phys. Letters125: 218
Hosoya H. (1986) Comp. & Maths. with Appls.12B: 271; reprinted in: Symmetry Unifying Human Understanding (Hagittai I., ed.). Pergamon Press, New York
Babić D., Graovac A. (1986) Croat. Chem. Acta59: 731
Bergan J. L., Cyvin B. N., Cyvin S. J. (1987) Acta Chim. Hung.124: 299
Cyvin S. J. (1988) Bull. Chem. Soc. Japan61: 4445
Cyvin S. J. (1988) Chem. Phys. Letters147: 384
Brunvoll J., Cyvin B. N., Cyvin S. J., Gutman I., Tošić R., Kovačević M. (1989) J. Mol. Struct. (Theochem)184: 165
Staab H. A., Diederich F. (1983) Chem. Ber.116: 3487
Staab H. A., Diederich F., Krieger C., Schweitzer D., Chem. Ber.116: 3504
Staab H. A., Diederich F., Čaplar V. (1983) Liebigs Ann. Chem.: 2262
Staab H. A., Sauer M. (1984) Liebigs Ann. Chem.: 742
Funhoff D. J. H., Staab H. A. (1986) Angew. Chem.98: 757
Gutman I., Trinajstić N. (1975) Croat. Chem. Acta47: 507
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)
Cvetković D., Doob M., Sachs H (1980) Spectra of Graphs—Theory and Application. Academic Press, New York
Trinajstić N. (1983) Chemical Graph Theory, Vols. I–II. CRC Press, Boca Raton, Fl.
Farrell E. J. (1979) Discrete Math.25: 121
Farrell E. J. (1979) J. Comb. Theory27B: 75
Gutman I. (1979) Match (Mülheim)6: 75
Godsil C. D., Gutman I. (1979) Z. Naturforsch.34a: 776
Godsil C. D., Gutman I. (1981) Croat. Chem. Acta54: 53
Godsil C. D., Gutman I. (1981) J. Graph Theory5: 137
Gutman I. (1977) Theor. Chim. Acta45: 309
Harary F., Schwenk A. J. (1973) Discrete Math.6: 359
Gutman I., El-Basil S. (1985) Z. Naturforsch.40a: 923
El-Basil S. (1987) J. Math. Chem.1: 153
El-Basil S. (1986) J. Chem. Soc., Faraday Trans. II82: 299
Cyvin S. J., Gutman I. (1988) Kekulé Structures in Benzenoid Hydrocarbons. Springer, Berlin Heidelberg New York Tokyo (Lecture Notes in Chemistry, Vol. 46)
Hosoya H., Yamaguchi T. (1975) Tetrahedron Letters: 4659
Gutman I., Cyvin S. J. (1989) Bull. Chem. Soc. Japan62: 1250
Ohkami N., Motoyama A., Yamaguchi T., Hosoya H., Gutman I. (1981) Tetrahedron37: 1113
Gutman I., El-Basil S. (1984) Z. Naturforsch.39a: 276
Aihara J. (1976) Bull. Chem. Soc. Japan49: 1429
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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