Supersymmetry of hexabenzocoronene torus

Croatica Chemica Acta

Volumn 77, Issue 1-2, 2004, Pages 89-95

  Hosoya, Haruo ^a   Tsukano, Yoko ^a   Nakada, Kyoko ^a,c   Iwata, Sayaka ^a   Nagashima, Umpei ^b  

^a OCHANOMIZU UNIVERSITY   (Japan)

^b NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^c AOYAMA GAKUIN UNIVERSITY   (Japan)

Author keywords

Degeneracy; Eigenvalue; Factorization; Graphite network; Group theory; Hexabenzocoronene; HMO; Secular determinant; Symmetry; Torus

Indexed keywords

CARBON; PYRENE DERIVATIVE;

ARTICLE; CHEMICAL STRUCTURE; MATHEMATICAL ANALYSIS; MOLECULAR DYNAMICS; STRUCTURE ANALYSIS; TECHNIQUE;

EID: 3042783592     PISSN: 00111643     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (41)

1. H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl, and R. E. Smalley, Nature (London) 318 (1985) 162-163.
2. S. Iijima, Nature (London) 354 (1991) 56-58.
3. T. G. Schmalz, W. A. Seitz, D. J. Klein, and G. E. Hite, J. Am. Chem. Soc. 110 (1988) 1113-1127.
4. H. W. Kroto, A. W. Allaf, and S. P. Balm, Chem. Rev. 91 (1991) 1213-1235.
5. E. C. Kirby, R. B. Mallion, and P. Pollak, J. Chem. Soc., Faraday Trans. 89 (1993) 1945-1953.
6. T. Pisansky, B. Plestenjak, and A. Graovac, Croat. Chem. Acta 68 (1995) 283-292.
7. M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, Science of Fullerenes and Carbon Nanotubes, Academic Press, New York, 1995.
8. M. Yoshida, M. Fujita, P. W. Fowler, and E. Kirby, J. Chem. Soc., Faraday Trans. 93 (1997) 1037-1043.
9. P. E. John, Croat. Chem. Acta 71 (1998) 435-447.
10. M. V. Diudea, I. Silaghi-Dumitrescu, and B. Parv, Commun. Math. Comput. Chem. (MATCH) 44 (2001) 117-133.
11. H. Hosoya, Y. Tsukano, M. Ohuchi, and K. Nakada, in: M. Doyama, J. Kihara, M. Tanaka, and R. Yamamoto (Eds.), Computer Aided Innovation of New Materials. II, Elsevier, Tokyo, 1993, pp. 155-158.
12. According to Prof. T. Enoki of Tokyo Institute of Technology the minimum number of carbon atoms of a clean sample of micro graphite to have as high electric conductivity as ordinary graphite would be more than hundred thousand. This experimentally derived number conforms to our estimate from HMO calculation.
13. N. Trinajstić, J. Math. Chem. 5 (1990) 171-175.
14. J. J. P. Stewart, J. Comput. Chem. 19 (1998) 168-180.
15. J.-I. Aihara, T. Yamabe, and H. Hosoya, Synth. Metals 64 (1994) 309-313.
16. Y. Tsukano, Master thesis, Ochanomizu Univ., 1994.
17. N. Hartsfield and G. Ringel, Pearls in Graph Theory. A Comprehensive Introduction: Academic Press, San Diego, 1994.
18. H. Hosoya, Y. Okuma, Y. Tsukano, and K. Nakada, J. Chem. Inf. Comput. Sci., 35 (1995) 351-356.
19. A. Takano and H. Hosoya, Natl. Sci. Rep. Ochanomizu Univ. 48 (1998) 45-80.
20. J. Xia and H. Hosoya, J. Chem. Inf. Comput. Sci. 42 (2002) 1004-1010.
21. E. Clar and C. T. Ironside, Proc. Chem. Soc. (1958) 150-150.
22. E. Clar, The Aromatic Sextet, John Wiley, London, 1972.
23. H. Hosoya and T. Yamaguchi, Tetrahedron Lett. (1975) 4659-4662.
24. M. Aida and H. Hosoya, Tetrahedron 36 (1980) 1317-1326.
25. N. Ohkami, A. Motoyama, T. Yamaguchi, H. Hosoya, and I. Gutman, Tetrahedron 37 (1981) 1113-1122.
26. C. A. Coulson and R. S. Rushbrooke, Proc. Cambridge Phil. Soc. 36 (1940) 193-200.
27. S. Iwata, Master thesis, Ochanomizu Univ., 1994.
28. The authors were given a hint of this property by Prof. J.-I. Aihara of Shizuoka Univ., to whom they give back their thanks.
29. D. J. Klein, J. Chem. Inf. Comput. Sci. 34 (1994) 453-459.
30. H. Hosoya and Y. Tsukano, Fullerene Sci. Technol. 2 (1994) 381-393.
31. A. J. Schwenk, in: Y. Alavi and D. R. Lick (Eds.), Theory and Applications of Graphs, Lecture Notes in Mathematics, Vol. 642, Springer, New York, 1978, pp. 516-533.
32. N. Biggs, Algebraic Graph Theory, Cambridge Univ. Press, London, 1974.
33. The term »topicity« is used in D. M. Walba, J. Simon, and F. Harary, Tetrahedron Lett. (1988) 731-734.
34. D. J. Klein, W. A. Seitz and T. G. Schmalz, J. Phys. Chem. 97 (1993) 1231-1236.
35. 29,36
36. A. Altschuler, Discrete Math. 1 (1972) 299-314, 4 (1973) 201-217.
37. A. Altschuler, Discrete Math. 1 (1972) 299-314, 4 (1973) 201-217.
38. C. Godsil and G. Royle, Algebraic Graph Theory, Springer, New York, 2001.
39. D. J. Klein and H. Zhu, Discrete Appl. Math. 67 (1996) 157-173.
40. M. Randic, Y. Tsukano, and H. Hosoya, Nat. Sci. Rep. Ochanomizu Univ. 45 (1994) 101-119.
41. E. C. Kirby, Croat. Chem. Acta 66 (1993) 13-26.