Complexity, sphericity, and ordering of regular and semiregular polyhedra

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Volumn 54, Issue 1, 2005, Pages 137-152

  Balaban, Alexandru T ^a   Bonchev, Danail ^b  

^a TEXAS A AND M UNIVERSITY AT GALVESTON   (United States)

^b VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27544432705     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (48)

1. Balaban, A. T.; Banciu, M.; Ciorba, V. Annulenes, Benzo-, Hetero-, Homo-Derivatives and Their Valence Isomers, CRC Press, Boca Raton, Florida, 1986, 3 volumes.
2. Waldrop, M. M. Complexity. The Emerging Science at the Edge of Order and Chaos. Touchstone/Simon and Schuster, New York, 1992.
3. Kaye, B. Chaos and Complexity. VCH Publishers, Weinheim, 1993.
4. Bovet, D. P.; Crescenzi, P. Introduction to the Theory of Complexity. Prentce-Hall, New York, 1994.
5. Rescher, N. Complexity: A Philosophical Overview. Transaction Publishers, New Brunswick, NJ, 1998, chapter 1, p. 1-24.
6. Nikolić, S.; Trinajstić, N.; Tolić, I. M.; Rücker, G.; Rücker, C. On molecular complexity indices. In Complexity in Chemistry. Introduction and Fundamentals. Bonchev, D.; Rouvray, D. H., Eds. Taylor and Francis, London, 2003, pp. 29-89.
7. Wolfram, S. A New Kind of Science. Wolfram Media, Inc., 2001, p. 735.
8. Nikolić, S.; Trinajstić, N.; Jurić, A.; Mihalić, Z.; Krilov, G. Complexity of some interesting (chemical) graphs. Croat. Chem. Acta, 1996, 69, 883-897.
9. Lukovits, I.; Nikolić, S.; Trinajstić, N. Resistance distance in regular graphs. Int. J. Quantum Chem. 1999, 71, 217-225.
10. Lukovits, I.; Nikolić, S.; Trinajstić, N. Note on the resistance distances in the dodecahedron. Croat. Chem. Acta, 2000, 73, 957-967.
11. Bonchev, D. On the complexity of Platonic solids. Croat. Chem. Acta, 2004, 77, 167-173.
12. Rücker, G.; Rücker, C. Counts of all walk as atomic and molecular descriptors. J. Chem. Inf. Comput. Sci., 1993, 33, 683-695.
13. Randić, M. On characterization of cyclic structures. J. Chem. Inf. Comput. Sci., 1997, 37, 1063-1071.
14. Rücker, G.; Rücker, C. Walk counts, labyrinthicity, and complexity of acyclic and cyclic graphs and molecules. J. Chem. Inf. Comput. Sci., 2000, 40, 99-106.
15. Babić, D.; Klein, D. J.; Lukovits, I.; Nikolić, S.; Trinajstić, N. Resistance-distance matrix: a computational algorithm and its application. Int. J. Quantum Chem. 2002, 90, 166-176.
16. http://mathworld.wolfram.com/SolidAngle.html
17. Balaban, A. T. Symmetry in chemical structures and reactions. Comps. and Maths. with Appls. 1986, 12B, 999-1020.
18. Reprinted in: Symmetry Unifying Human Understanding (Hargittai, I., editor), Pergamon Press, New York, 1986, pp. 999-1020.
19. CRC Concise Encyclopedia of Mathematics. Boca Raton, Florida.
20. th ed., Wiley, New York, 1999, pp. 9, 135.
21. Schultz, H. P. Topological organic chemistry. Polyhedranes and prismanes. J. Org. Chem. 1965, 30, 1361-1364.
22. n: n = 4, 6, 8, 10, 12, 16, 20, 24). J. Phys. Chem. A 2000, 104, 6622-6627.
23. Balaban, A. T. Theoretical investigations on single-wall nanocones. In: Nanostructures. Novel Architecture (M. Diudea, Ed.), Nova Publishers, 2005, pp. 113-142.
24. 60: a new form of carbon. Nature, 1990, 347, 354-358.
25. 60. Science, 2002, 295, 1500-1503.
26. Scott, L. T. Methods for the chemical synthesis of fullerenes. Angew. Chem.Int. Ed. 2004, 43, 4994-5007.
27. Osawa, E. Kagaku (Kyoto) 1970, 25, 854;
28. Yoshida, Z.; Osawa, E., Aromaticity. Kagakudojin, Kyoto, 1971.
29. Davidson, R. A. Unified theory of graph spectral reduction networks. 4. Spectral analysis of graphs by cyclic automorphisms groups. Theor. Chim. Acta, 1981, 58, 193-231.
30. Bochvar, D. A.; Gal'pern, E. G. Truncated dodecahedron and truncated icosahedron hypothetical structures, Dokl. Akad Nauk SSSR, 1973, 209, 610-612;
31. Stankevich, I. V.; Nikerov, M. V.; Bochvar, D. A. The structural chemistry of crystalline carbon: geometry, stability and electronic spectrum. Usp. Khim. 1984, 53, 1101-1121 (in Russian).
32. de La Vaissière, B.; Fowler, P.W.; Deza, M. Codes in Platonic, Archimedean, Catalan, and related polyhedra: a model for maximum addition patterns in chemical cages. J. Chem. Inf. Comput. Sci. 2001, 41, 736-386.
33. 2m. Chem. Phys. Lett. 1999, 312, 77-84.
34. Balaban, A. T.; Klein, D. K.; Ivanciuc, O. Large "pillow" fullerenes hydrogenated at the inter-sheet "seam". Fullerenes, Nanotubes and Carbon Nanostructures, in press.
35. Coulombeau, C.; Rassat, A. Simple geometric potential calculations of vibrational frequencies of saturated hydrocarbons hgaving the structure of regular and semiregular polyhedra. J. Chim. Phys. Phys.-Chim. Biol., 1988, 85, 369-374 (in French).
36. Moran, D.; Manoharan, M.; Heine, T.; Schleyer, P. v. R. σ-Antiaromaticity in cyclobutane, cubane, and other molecules with saturated four-membered rings. Org. Lett. 2003, 5, 23-26.
37. Wang, Z.; Schleyer, P. v. R., A "sea-urchin" family of boranes and carboranes: the 6m + 2n electron rule. J. Am. Chem. Soc. 2003, 125, 10484-10485.
38. Maier, G.; Rang, H.; Born, D. Stabilization of cage compounds through steric hindrance by tert-butyl groups. In: Cage Hydrocarbons (G. A. Olah, Ed.), Wiley, New York, 1990, pp. 219-259.
39. Eaton, P. E.; Cole, T. W. The cubane system. J. Am. Chem. Soc. 1964, 86, 52-54.
40. Paquette, L. A. The [n]peristylane-polyhedrane connection. In: Cage Hydrocarbons (G. A. Olah, Ed.), Wiley, New York, 1990, pp. 313-352.
41. Fessner, W.-D.; Prinzbach, H. The pagodane route to dodecahedrane. In: Cage Hydrocarbons (G. A. Olah, Ed.), Wiley, New York, 1990, pp. 353-405.
42. Saunders, M. Buckminsterfullerane: the inside story. Science, 1991, 253, 330-331.
43. 36. J. Phys. Chem. 1991, 95, 5763-5768.
44. 60 molecules. Chem.Phys. Lett. 1991, 181, 68-72.
45. Cioslowski, J.; Edgington, L.; Stefanov, B. B. Steric overcrowding in perhalogenated cyclohexanes, dodecahedranes, and [60]fulleranes. J. Am. Chem. Soc. 1995, 117, 10381-10384.
46. n (X = H, F; n = 2, 36, 60). Chem.Phys. Lett. 1992, 193, 236-242.
47. 60 and monoalkylated perhydrogenated fullerenes. Chem.Phys. Lett. 1961, 249, 406-412.
48. 60. J. Phys. Chem. A, 2001, 105, 7634-7637.