An upper bound for the Clar number of fullerene graphs

Journal of Mathematical Chemistry

Volumn 41, Issue 2, 2007, Pages 123-133

  Zhang, Heping ^a   Ye, Dong ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

Carbon nanotube; Clar formula; Clar number; Fullerene graph; Kekul structure; Perfect matching; Sextet pattern

Indexed keywords

EID: 33847671465     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-006-9061-5     Document Type: Article

References (22)

1. 60: Buckminsterfullerene, Nature 318 (1985) 162-163.
2. 60: a new form of carbon, Nature 347 (1990) 354.
3. 70: the third form of carbon, J. Chem. Soc. Chem. Commum. (1990) 1423.
4. P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes (Oxford Univ. Press, Oxford, 1995).
5. G. Brinkmann and A. Dress, A constructive enumeration of fullerenes, J. Algorithms 23 (1997) 345-358.
6. E. Clar, The Aromatic Sextet (Wiley, New York, 1972).
7. P. Hansen and M. Zheng, Upper bounds for the Clar number of benzenoid hydrocarbons, J. Chem. Soc. Faraday Trans. 88 (1992) 1621-1625.
8. P. Hansen and M. Zheng, The Clar number of a benzenoid hydrocarbon and linear programming, J. Math. Chem. 15 (1994) 93-107.
9. H. Abeledo and G. Atkinson, The Clar and Fries problems for benzenoid hydrocarbons are linear programs, in: Discrete Mathematical Chemistry, DIMACS Series, Vol. 51, eds. P. Hansen, P. Fowler and M. Zheng (American Mathematical Society, Providence, RI, 2000), pp. 1-8.
10. S. Klavžar, P. Žigert and I. Gutman, Clar number of catacondensed benzenoid hydrocarbons, J. Mol. Struct. (Theochem) 586 (2002) 235-240.
11. K. Salem and I. Gutman, Clar number of hexagonal chains, Chem. Phys. Lett. 394 (2004) 283-286.
12. F. Zhang and X. Li, The Clar formulas of a class of hexagonal systems, Match 24 (1989) 333-347.
13. H. Zhang, The Clar formula of a type of benzenoid systems, J. Xinjiang Univ. (Natural Science, In Chinese) 10 (1993) 1-7.
14. H. Zhang, The Clar formula of hexagonal polyhexes, J. Xinjiang Univ. (Natural Science) 12 (1995) 1-9.
15. H. Zhang, The Clar formula of regular t-tier strip benzenoid systems, Sys. Sci. Math. Sci. 8(4) (1995) 327-337.
16. F. Zhang and L. Wang, k-resonance of open-end carbon nanotubes, J. Math. Chem. 35(2) (2004) 87-103.
17. 60), J. Mol. Struct. (Theochem) 531 (2000) 9-21.
18. W.C. Shiu, P.C.B. Lam and H. Zhang, Clar and sextet polynomials of buckminsterfullerene, J. Mol. Struct. (Theochem) 662 (2003) 239-248.
19. H. Zhang and J. He, A comparison between 1-factor count and resonant pattern count in plane non-bipartite graphs, J. Math. Chem. 38(3) (2005) 315-324.
20. I. Gutman and S.J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons (Springer-Verlag, Berlin, 1989).
21. T. Došlić, Cyclical edge-connectivity of fullerene graphs and (k,6)-cages, J. Math. Chem. 33 (2003) 103-112.
22. R. Saito, M.S. Dresselhaus and G. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).