Towards a combinatorial efficient algorithm to solve the Clar problem of benzenoid hydrocarbons

Match

Volumn 53, Issue 2, 2005, Pages 419-426

  Salem, Khaled ^a  

^a The George Washington University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27544436329     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Abeledo, H., Atkinson, G., The Clar and Fries problems for benzenoid hydrocarbons are linear programs in: Hansen, P., Fowler, P., Zheng, M. (Eds.), Discrete Mathematical Chemistry, Am. Math. Soc., Providence, RI, (2000) 1-8.
2. Atkinson, G., Combinatorial optimization on planar bipartite graphs via unimodular matrices, DSc dissertation, The George Washington University, 1998.
3. Clar, E., The Aromatic Sextet, Wiley, London, 1972.
4. Cook, W.J.; Cunnigham, W.H; Pulleyblank, W.R.; Schrijver, A., Combinatorial Optimization, Wiley, New York, 1998.
5. Fleischner, H., Eulerian graphs and related topics- Part 1, Volume 1, North- Holland, Amsterdam, 1990.
6. Gallai, T., Über extreme Punkt- und Kantenmengen, Ann. Univ. Sci. Budapest, Eötvös Sect. Math. 2 (1959) 133-138.
7. Guo, X. F., Zhang, F.J., Mathematical properties and structures of sets of sextet patterns of generalized polyhexes, J. Math. Chem. 9 (1992) 279-290.
8. Gutman, I., Topological properties of benzenoid molecules, Bull. Soc. Chim. Beograd 47 (1982) 453-471.
9. Gutman, I., Topological properties of benzenoid systems. XIX. Contributions to the aromatic sextet theory, Wiss. Z. Thechn. Hochsch. Ilmenau 29 (1983) 57-65.
10. Gutman, I.; Hosoya, H.; Yamaguchi, T.; Motoyama, A.; Kuboi, N., Topological properties of benzenoid systems. III. Recursion relation for the sextet polynomial, Bull. Soc. Chim. Beograd 42 (1977) 503-510.
11. Gutman, I. and Cyvin, S.J., Introduction to the theory of benzenoid hydrocarbons, Springer, Berlin, 1989.
12. Hansen, P., Zheng, M.L., Upper bounds for the Clar number of a benzenoid hydrocarbon, J. Chem. Soc. Faraday Trans. 88 (1992) 1621-1625.
13. Hansen, P., Zheng, M., The Clar number of a benzenoid hydrocarbon and linear programming, J. Math. Chem. 15 (1994) 93-107.
14. Harary, F., Graph Theory, Addison-Wesley, Reading, 1969.
15. Hosoya, H., Yamaguchi, T., Sextet polynomial. A new enumeration and proof technique for the resonance theory applied to the aromatic hydrocarbons, Tetrahedron Lett. 52 (1975) 4659-4662.
16. Klavžar, S., private communication, (2003).
17. Klavžar, S.; Žigert, P.; Gutman, I., Clar number of catacondensed benzenoid hydrocarbons, J. Mol. Struct. (Theochem) 586 (2002) 235-240.
18. Ohkami, N., Motoyama, A., Yamaguchi, T., Hosoya, H., Gutman, I., Graph-theoretical analysis of the Clar's aromatic sextet, Tetrahedron 37 (1981) 1113-1122.
19. Zhang, F.J., Li, X.L., Clar formula of a class of hexagonal systems, MATCH Commun. Math. Comput. Chem. 24 (1989) 333-347.
20. Zhang, H., Zhang, F., The rotation graphs of perfect matchings of plane bipartite graphs, Discr. Appl. Math. 73 (1997) 5-12.