On the complexity of fullerenes and nanotubes

Complexity in Chemistry, Biology, and Ecology

Volumn , Issue , 2005, Pages 1-48

  Randić, Milan ^a,b   Guo, Xiaofeng ^b,c   Plavšić, Dejan ^d   Balaban, Alexandru T ^e  

^a NATIONAL INSTITUTE OF CHEMISTRY   (Slovenia)

^b DRAKE UNIVERSITY   (United States)

^c XIAMEN UNIVERSITY   (China)

^d RUDER BO KOVI INSTITUTE   (Croatia)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747756161     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/0-387-25871-X_1     Document Type: Chapter

References (120)

1. H. Primas, Chemistry, Quantum Mechanics and Reductionism (Perspectives in Theoretical Chemistry), 2nd ed, Springer, Berlin (1983) p. 292.
2. M. Randíc and D. Plavsíc, Int. J. Quantum Chem. 91, 20-31 (2003).
3. M. Randíc and D. Plavsíc, Croat. Chem. Acta 75, 107-116 (2002).
4. R. Barone and M. Chanon, J. Chem. Inf. Comput. Sci. 41, 269-272 (2001).
5. D. Bonchev, J. Chem. Inf. Comput. Sci. 40, 934-941 (2000).
6. S. Nikolíc,N.Trinajstíc and I.M. Tolíc, J. Chem. Inf. Comput. Sci. 40, 920-926 (2000)
7. S Nikolíc, IM Tolíc and N Trinajstíc, MATCH Commun. Math. Comput. Chem. 40, 187-201 (1999).
8. G. Rücker and C. Rücker, J. Chem. Inf. Comput. Sci. 40, 99-106 (2000).
9. S.H. Bertz, Bull. Math. Biol. 45, 849-855 (1983).
10. S.H. Bertz, J. Am. Chem. Soc., 103, 3599-3601 (1981).
11. S.H. Bertz, in: Chemical Applications of Topology and Graph Theory, R B King, (ed.), Elsevier, New York (1983) p. 206-221.
12. H. Wiener, J. Am. Chem. Soc. 69, 17-20 (1947).
13. P.E. John, R.B. Mallion and I. Gutman, J. Chem. Inf. Comput. Sci. 38, 108-112 (1998).
14. I. Gutman, R. B. Mallion and J.W. Essam, Mol. Phys. 50, 859-877 (1983).
15. S Nikolíc, N Trinajstíc, A Juríc, Z Mihalíc and G Krilov, Croat. Chem. Acta 69, 883-897 (1996).
16. M. Randíc, G. M. Brissey, R. G. Spencer and C. L. Wilkins, Computers & Chem. 3, 5-13 (1979).
17. A. Mowshowitz, Bull. Math. Biophys. 30, 175-204 (1968).
18. C. Shannon andW.Weaver, Mathematical Theory of Communications, University of Illinois Press, Urbana, IL (1949).
19. D. Bonchev and O. E. Polansky, in Graph Theory and Topology in Chemistry, R. B. King and D. H. Rouvray, (eds.), Elsevier, Amsterdam (1987) p. 126-158.
20. H. Primas, Chemistry, Quantum Mechanics and Reductionism (Perspectives in Theoretical Chemistry), 2nd ed., Springer, Berlin (1983) p. 254.
21. R. Hoffmann, Am. Sci. 76, 182-185 (1988).
22. M. Randíc, Chem. Rev. 103, 3449-3605 (2003).
23. M. Randíc, Chem. Phys. Lett. 38, 68-70 (1976)
24. M. Randíc, J. Am. Chem. Soc. 99, 444-450 (1977).
25. F. Harary, Graph Theory, Addison-Wesley, Reading, MA (1969).
26. M. Randíc, in: The Encyclopedia of Computational Chemistry, P. V. R. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P A. Kollman, H. F. Schaefer III and P. R. Schreiner (eds.), Wiley, Chichester, p. 3018-3032.
27. A.T. Balaban, Highly Discriminating Distance-BasedTopological Index. Chem. Phys. Lett. 80, 399-404 (1982).
28. J. Devillers and A. T. Balaban (eds.), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, The Netherlands (1999).
29. M. Randíc, J. Am. Chem. Soc. 97, 6609-6615 (1975).
30. M. Randíc, J. Mol. Graphics Model. 20, 19-35 (2001).
31. H. L. Morgan, J. Chem. Docum. 5, 107-113 (1965).
32. M. Razinger, Theor. Chim. Acta, 61, 581-586 (1982).
33. J. Figueras, J. Chem. Inf. Comput. Sci. 33, 717-718 (1993).
34. G. Rücker and C. Rücker, J. Chem. Inf. Comput. Sci. 33, 683-695 (1993).
35. G. Rücker and C. Rücker, J. Chem. Inf. Comput. Sci. 41, 1457-1462 (2001).
36. F. Ayers, Jr., Theory and Problems of Matrices, Schaum, New York (1962) p. 181.
37. D. M. Cvetkovíc and I. Gutman, Croat. Chem. Acta, 49, 115-121 (1977).
38. L. Lovasz and J. Pelikan, Period. Math. Hung. 3, 175-182 (1973).
39. Comment by a referee.
40. E. Ruch and I. Gutman, J. Comb. Inf. System Sci. 4, 285-295 (1979).
41. M. Randíc, J. Zupan, M. Novic, B. D. Gute and S. C. Basak, SAR&QSAR in Environ. Res. 13, 689-703 (2002).
42. M. Randíc, M. Novic and M. Vracko, Eigenvalues as Molecular Descriptors, in: QSPR/QSAR Studies by Molecular Descriptors, M. V. Diudea (ed.), Nova Science, Huntington, NY (2002) p. 147-211.
43. D. J. Klein, J. Chem. Edu. 69, 691 (1992).
44. D. J. Klein and D. Babíc, J. Chem. Inf. Comput. Sci. 37, 656-671 (1997).
45. M. Randíc, Chem. Rev., 103, 3449-3605 (2003).
46. M. Randíc, Croat. Chem. Acta 66, 289-312 (1993).
47. S. Nikolíc, N. Trinajstíc, I. M. Tolíc, G. Rücker and C. Rücker, On Molecular Complexity Indices, in: Complexity in Chemistry. D. H. Rouvray and D. Bonchev (eds.), Francis & Taylor, London (2003);
48. (b) A. T. Balaban, A Comparison Between Various Topological Indices, Particularly Index J andWiener's IndexWin: Topology in Chemistry: Discrete Mathematics of Molecules, D. H. Rouvray and R. B. King (eds.) Horwood, Chichester (2002) pp. 89-112;
49. (c) A. T. Balaban, D. Mills, and S. C. Basak, MATCH Commun. Math. Comput. Chem. 45, 5-26 (2002).
50. M. Randíc, J. Math. Chem. 25, 345-358 (1998).
51. M. Randíc, M. Razinger and D. Plavsíc, MATCH Commun. Math. Comput. Chem. 35, 243-259 (1997).
52. M. Randíc, N Basak and D Plavsíc, Croat. Chem. Acta 77, 251-257 (2004).
53. D. Bonchev, The Problems of Computing Molecular Complexity. in: Computational Chemical Graph Theory, D. H. Rouvray (ed.) Nova, Commack, NY (1990) p. 33-63
54. D. Bonchev, Overall Connectivity and Topological Complexity: A New Tool for QSPR/QSAR., in: Topological Indices and Related Descriptors in QSAR and QSPR, J. Devillers and A. T. Balaban (eds.), Gordon and Breach, The Netherlands (1999), p. 361-401
55. D. Bonchev and W. A. Seitz, The Concept of Complexity in Chemistry. in: Concepts in Chemistry-A Contemporary Challenge, D. H. Rouvray (ed.), Wiley, New York (1997) p. 353-381
56. D. Bonchev, Shannon's Information and Complexity, in: Complexity in Chemistry. Introduction and Fundamentals, D. Bonchev and D H. Rouvray (eds.), Taylor and Francis, London (2003) p. 157-187
57. D. Bonchev, MATCHCommun. Math. Comput. Chem. 7, 65-113 (1979)
58. D. Bonchev, Bulg. Chem. Commun. 28, 567-582 (1995)
59. D. Bonchev,SARQSAREnviron. Res. 7, 23-43 (1997)
60. D. Bonchev, Croat. Chem. Acta 77, 167-173 (2004).
61. M. Randíc, Croat. Chem. Acta 74, 683-705 (2001).
62. T. Laidboeur, D. Cabrol-Bass and O. Ivanciuc, J. Chem. Inf. Comput. Sci. 36, 811-821 (1996).
63. For a complete list of fullerenes and their symmetries, see: P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Oxford, Clarendon (1995).
64. R. F. Muirhead, Proc. Edinburgh Math. Soc. 21, 144-157 (1903).
65. Special issue of MATCH Commun. Math. Comput. Chem. 42, 1-290 (2000).
66. D. J. Klein, MATCH Commun. Math. Comput. Chem. 42, 7-31 (2000).
67. S. H. Bertz and C. M. Zamfirescu, MATCH 42, 39-70 (2000).
68. M. Randíc, M. Novic and M. Vracko, MATCH 42, 39-231 (2000).
69. S. El-Basil, MATCH Commun. Math. Comput. Chem. 42, 233-259 (2000).
70. D. J. Klein and L. Bytautas, MATCH Commun. Math. Comput. Chem. 42, 261-290 (2000).
71. K. Vogt and G. Welz, Order Theoretical Tools in Environmental Sciences, Shaker, Aachen (2002).
72. M. Randíc, Chem. Phys. Lett. 55, 547-551 (1978).
73. J. Karamata, Publ. Math. Univ. Belgrade 1, 145 (1932).
74. E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, 1961.
75. G. H Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, London (1934).
76. F. A. Cotton, G. Wilkinson, C. A. Murillo and M. Bochmann, Advanced Inorganic Chemistry, 6th ed., Wiley, New York, pp. 131-157, 168-180.
77. F. A. Cotton, G. Wilkinson, C. A. Murillo and M. Bochmann, Advanced Inorganic Chemistry, 6th ed., Wiley, New York, pp. 265-280.
78. A. T. Balaban, D. Oniciu and A. R. Katritzky, Chem. Revs. 104, 000 (2004).
79. A. T. Balaban, C. C. Rentea and E. Ciupitu, Rev. Roum. Chim. 13, 231-247; Erratum, ibid., p. 1233 (1968).
80. H. Zhu, A. T. Balaban, D. J. Klein, and T. P. Zivkovíc, J. Chem. Phys. 101, 5281-5292 (1994).
81. A. T. Balaban, Theoretical Investigation of Carbon Nets and Molecules, in: Theoretical Organic Chemistry, C. Parkanyi (ed.), Elsevier, Amsterdam (1998), p. 381-404.
82. A. T. Balaban, Computers Math. Applic. 17, 397-416 (1989)
83. Reprinted in: Symmetry II, I Hargittai (ed.), Pergamon Press, Oxford (1989) p. 397-416.
84. K. M. Merz Jr, R. Hoffmann and A. T. Balaban, J. Am. Chem. Soc. 109, 6742-6751 (1987).
85. A. T. Balaban, D. J. Klein and C. A. Folden, Chem. Phys. Lett. 217, 266-270 (1994).
86. A. T. Balaban, D. J. Klein, andW. A. Seitz, Intern. J. Quantum Chem. 60, 1065-1068 (1996).
87. A. T. Balaban and D. J. Klein, Carbon 35, 247-251 (1997).
88. A. T. Balaban, D. J. Klein, and X. Liu, Carbon 32, 357-359 (1994).
89. M. H. Ge and K. Sattler, Chem. Phys. Lett. 220, 3-5 (1964).
90. H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl, and R. E. Smalley, Nature 318, 162-163 (1985).
91. W. Krätschmer, L. D. Lamb, K. Fostiropoulos, and D. R. Huffman, Nature 347, 354-358 (1990).
92. S. Ijima, Nature 354, 56-58 (1991).
93. T. W. Ebbesen and P. M. Ajayan, Nature 358, 220-222 (1992).
94. R. N. Kostoff, T. Braun, A. Schubert, D. R. Toothman, and J. A. Humenik, J. Chem. Inf. Comput. Sci. 40, 19-39 (2000).
95. D. J. Klein, W. A. Seitz, and T. G. Schmalz, J. Phys. Chem. 97, 1231-1236 (1993).
96. A. T. Balaban, MATCH Commun. Math. Comput. Chem. 33, 25-33 (1996).
97. A. T. Balaban, Bull. Soc. Chim. Belges 105, 383-389 (1996).
98. H. Y. Zhu, D. J. Klein, T. G. Schmalz, J. Phys. Chem. Solids 59, 417-423 (1998)
99. D. J. Klein and L. Bytautas, J. Phys. Chem. A 103, 5196-5210 (1999)
100. O. Ivanciuc, D. J. Klein and L Bytautas, Carbon 40, 2063-2083 (2002).
101. I. Lukovits, A. Graovac, E. Kálmán, G. Kaptay, P. Nagy, S. Nikolic, J. Sytchev, and N. Trinajstic, J. Chem. Inf. Comput. Sci. 43, 609-614 (2003).
102. M. V. Diudea, T. S. Balaban, E. C. Kirby, and A. Graovac, Phys. Chem. Chem. Phys. 5, 4210-4214 (2003).
103. M. V. Diudea, M. Stefu, B. Parv, and P. E. John, Croat. Chem. Acta 77, 111-115 (2004);
104. M. V. Diudea, Carbon Nanostruct. 10, 273-292, 2002
105. MV Diudea, Topology of Naphthylenic Tori. Phys. Chem. Chem. Phys. 4, 4740-4746 (2002).
106. M. Diudea, I. Silaghi-Dumitrescu, and B. Parv, Internet Electronic J. Mol. Design 1, 10-22 (2002).
107. E. C. Kirby, RecentWork on Toroidal and Other Exotic Fullerene Structures, in: From Chemical Topology to Three-Dimensional Geometry,AT Balaban (ed.), Plenum Press, New York (1997) p. 263-296.
108. M. Terrones,W. K. Hsu, J. P. Hare, H.W. Kroto, H. Terrones and DRMWalton, Phil. Trans. Roy. Soc. London A 354, 2025-2054 (1996).
109. S. Ihara, S. Itoh, and J. I. Kitakami, Phys. Rev. B 47, 12 908-12 911 (1993).
110. M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, Science of Fullerenes and Carbon Nanotubes, Academic Press, San Diego, CA (1996) p. 756.
111. J. Liu, H. Dai, J. H. Hafner, D. T. Colbert, R. E. Smalley, S. J. Tans, and C Dekker, Nature 385, 780-781 (1997).
112. B. I. Dunlap, Phys. Rev. B 46, 1933-1936 (1992).
113. S. Ihara, S. Itoh, and J. Kitakami, Phys. Rev. B 48, 5643-5647 (1993).
114. L. P. Biro, G. I. Mark, and P. Lambin, IEEE Trans. Nanotechnol. 2, 362-367 (2003).
115. G. E. Scuseria, Chem. Phys. Lett. 195, 534-536 (1992).
116. A. N. Andriotis, M. Menon, D. Srivastava and L. A. Chernozatonskii, Phys. Rev. Lett. 87, 066 802-1-066 802-4 (2001).
117. J. A. Jaszczak, G. W. Robinson, S. Dimovski and Y. Gogotsi, Carbon 41, 2085-2092 (2003).
118. G. Zhang, X. Jiang and E. Wang, Science 300, 472-474 (2003).
119. P. E. Lammert and V. H. Crespi, Phys. Rev. Lett. 85, 5190-5193 (2000).
120. M. M. J. Treacy and J. Kilian, Mat. Res. Soc. Symp. Proc. 675, 1-6 (2001).