A Special Form of Numerical Self-Similarity of Kekulé Counts of Benzenoid Hydrocarbons

Croatica Chemica Acta

Volumn 71, Issue 1, 1998, Pages 1-20

  El Basil, Sherif ^a  

^a CAIRO UNIVERSITY   (Egypt)

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EID: 0347663703     PISSN: 00111643     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. S. El-Basil, Croat. Chem. Acta 69 (1996) 1117.
2. S. El-Basil, J. Chem. Soc., Trans. Faraday 89 (1993) 909.
3. S. El-Basil, J. Chem. Soc., Trans. Faraday 90 (1994) 2201.
4. S. El-Basil, J. Mol. Struct. (Theochem.) 288 (1993) 67.
5. S. El-Basil, J. Mol. Struct. (Theochem) 313 (1994) 237.
6. S. El-Basil, J. Math. Chem. 14 (1993) 305.
7. 1 circuit contains 4j + 2 pi - elelctrons. (see Ref. 4).
8. 1 circuit contains 4j + 2 pi - elelctrons. (see Ref. 4).
9. 1 circuit contains 4j + 2 pi - elelctrons. (see Ref. 4).
10. The concept of graph-generation is considered in: M. Randić, W. L. Woodworth, A. F. Kleiner, and H. Hosoya, J. Comput. Chem. 8 (1987) 522.
11. 4 »cubane« linked by SR bridges [D. M. P. Mingos and D. J. Wales, Introduction to Cluster Chemistry, Prentice Hall, Englewood Cliffs, 1990, pp. 24, 27, 62, 76]. The graph generation uncovered by the ℓ-operation also led to an analogy with Feigenbaum's theory of chaos [see Ref. 5, and M. Feigenbaum, J. Stat. Phys. 19 (1978) 25].
12. 4 »cubane« linked by SR bridges [D. M. P. Mingos and D. J. Wales, Introduction to Cluster Chemistry, Prentice Hall, Englewood Cliffs, 1990, pp. 24, 27, 62, 76]. The graph generation uncovered by the ℓ-operation also led to an analogy with Feigenbaum's theory of chaos [see Ref. 5, and M. Feigenbaum, J. Stat. Phys. 19 (1978) 25].
13. 4 »cubane« linked by SR bridges [D. M. P. Mingos and D. J. Wales, Introduction to Cluster Chemistry, Prentice Hall, Englewood Cliffs, 1990, pp. 24, 27, 62, 76]. The graph generation uncovered by the ℓ-operation also led to an analogy with Feigenbaum's theory of chaos [see Ref. 5, and M. Feigenbaum, J. Stat. Phys. 19 (1978) 25].
14. 4 »cubane« linked by SR bridges [D. M. P. Mingos and D. J. Wales, Introduction to Cluster Chemistry, Prentice Hall, Englewood Cliffs, 1990, pp. 24, 27, 62, 76]. The graph generation uncovered by the ℓ-operation also led to an analogy with Feigenbaum's theory of chaos [see Ref. 5, and M. Feigenbaum, J. Stat. Phys. 19 (1978) 25].
15. On the other hand, deterministic fractals have been considered by D. J. Klein, J. J. Cravey, and G. E. Hite, Polycyclic Aromat. Compd. 2 (1991) 165; D. Plavšić, N. Trinajstić, and D. J. Klein, Croat. Chem. Acta 65 (1992) 279.
16. On the other hand, deterministic fractals have been considered by D. J. Klein, J. J. Cravey, and G. E. Hite, Polycyclic Aromat. Compd. 2 (1991) 165; D. Plavšić, N. Trinajstić, and D. J. Klein, Croat. Chem. Acta 65 (1992) 279.
17. All-kinked benzenoids include, in addition to the polyphenanthrenoid polyphenes (which are traditionally called zigzag polyacenes such as phenanthrene, chrysene, pentacene,...), all possible isoarithmic benzenoids: See e.g. S. J. Cyvin and I. Gutman, Lecture Notes in Chemistry 46 (1988) 29. Isoarithmicity is considered in; A. T. Balaban and I. Tomescu, MATCH, 14 (1983) 155. For instance, there are three isoarithmic all-kinked benzenoids (the K values of any of which is 13). The molecular graphs of these benzenoids are shown below. (matrix presented)
18. All-kinked benzenoids include, in addition to the polyphenanthrenoid polyphenes (which are traditionally called zigzag polyacenes such as phenanthrene, chrysene, pentacene,...), all possible isoarithmic benzenoids: See e.g. S. J. Cyvin and I. Gutman, Lecture Notes in Chemistry 46 (1988) 29. Isoarithmicity is considered in; A. T. Balaban and I. Tomescu, MATCH, 14 (1983) 155. For instance, there are three isoarithmic all-kinked benzenoids (the K values of any of which is 13). The molecular graphs of these benzenoids are shown below. (matrix presented)
19. D. Sechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53 (1984) 1951. See also Refs. 2, 3.
20. D. Stauffer, Introduction to Percolation Theory, Taylor and Francis, London, 1985.
21. See, e.g., H.-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Crystals, Springer-Verlag, New York, 1992, p. 471.
22. S. J. Cyvin and I. Gutman, Lecture Notes in Chemistry 46 (1988) 41.
23. S. J. Cyvin and I. Gutman, Lectures in Chemistry 46 (1988) 69.
24. I. Gutman and S. El-Basil, Chem. Phys. Lett. 115 (1985) 416.
25. S. El-Basil, J. Math. Chem. 1 (1987) 153; S. El-Basil and M. Randić, Adv. Quantum Chem. 24 (1992) 239.
26. S. El-Basil, J. Math. Chem. 1 (1987) 153; S. El-Basil and M. Randić, Adv. Quantum Chem. 24 (1992) 239.
27. I. Gutman and S. J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons, Springer Verlag, New York, 1989, p. 56.