Relations between Clar structures, Clar covers, and the sextet-rotation tree of a hexagonal system

Discrete Applied Mathematics

Volumn 156, Issue 10, 2008, Pages 1809-1821

  Zhou, Shan ^a   Zhang, Heping ^a   Gutman, Ivan ^b  

^a LANZHOU UNIVERSITY   (China)

^b Faculty of Science   (Serbia)

Author keywords

Clar cover; Clar structure; Hexagonal system; Perfect matching; Sextet rotation tree

Indexed keywords

(N-1) CRITERION; HEXAGONAL SYSTEMS; NECESSARY AND SUFFICIENT CONDITIONS; PERFECT MATCHINGS;

EID: 45849102068     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2007.08.047     Document Type: Article

References (27)

1. Chen Z. Directed tree structure of the set of Kekulé patterns of polyhex graphs. Chem. Phys. Lett. 115 (1985) 291-293
2. Cyvin S.J., and Gutman I. Kekulé Structures in Benzenoid Hydrocarbons (1988), Springer, Berlin
3. El-Basil S. Combinatorial Clar sextet theory. Theor. Chim. Acta 70 (1986) 53-65
4. Guo X., and Zhang F. An efficient algorithm for generating all Kekulé patterns of a generalized benzenoid system. J. Math. Chem. 12 (1993) 163-171
5. Gutman I. Covering hexagonal systems with hexagons. Proceedings of the 4th Yougoslav seminar on Graph theory. Novi Sad (1983) 51-60
6. Gutman I., and Cyvin S.J. Introduction to the Theory of Benzneoid Hydrocarbons (1989), Springer, Berlin
7. Gutman I., Hosoya H., Yamaguchi T., Motoyama A., and Kuboi N. Topological properties of benzenoid systems. III. Recursion method for the sextet polynomial. Bull. Soc. Chim. Beograd 42 (1977) 503-510
8. Gutman I., Teodorović A.V., and Kolaković N. Algebraic studies of Kekulé structures, A semilattice based on the sextet rotation concept. Z. Naturforsch 44a (1989) 1097-1101
9. Gutman I., Teodorović A.V., and Kolaković N. An application of corals. J. Serb. Chem. Soc. 55 (1990) 363-368
10. He W.C., and He W.J. Some topological properties of normal benzenoids and coronoids. MATCH Commun. Math. Comput. Chem. 25 (1990) 225-236
11. Herndon W.C., and Hosoya H. Parameterized valence bond calculations for benzenoid hydrocarbons using Clar structure. Tetrahedron 40 (1984) 3987-3995
12. Lovász L., and Plummer M.D. Matching Theory (1986), North-Holland, Amsterdam
13. Ohkami N., Motoyama A., Hosoya H., and Gutman I. Graph-theoretical analysis of the Clar's aromatic sextet. Tetrahedron 37 (1981) 1113-1122
14. Randić M., and El-Basil S. Graph theoretical analysis of large benzenoid hydrocarbons. J. Mol. Struct. (Theochem) 303 (1994) 233-245
15. Randić M., El-Basil S., Nikolić S., and Trinajstić N. Clar polynomial of large benzenoid systems. J. Chem. Inf. Comput. Sci. 38 (1998) 536-574
16. Sachs H. Perfect matchings in hexagonal systems. Combinatorica 4 (1984) 89-99
17. Schaad L.J., and Hess B.A. Dewar resonance energy. Chem. Rev. 101 (2001) 1465-1476
18. Shiu W.C., Lam P.C.B., and Zhang H. Clar and sextet polynomials of buckminsterfullerene. J. Mol. Struct. (Theochem) 622 (2003) 239-248
19. Shiu W.C., Lam P.C.B., Zhang F., and Zhang H. Normal components, Kekulé patterns and Clar patterns in plane bipartite graphs. J. Math. Chem. 31 (2002) 405-420
20. Swinborne-Sheldrake R., Herndon W.C., and Gutman I. Kekulé structures and resonance energies of benzenoid hydrocarbons. Tetrahedron Lett. 16 (1975) 755-758
21. Zhang F., and Chen R. A theorem concerning polyhex graphs. MATCH Commun. Math. Comput. Chem. 19 (1986) 179-188
22. Zhang F., and Chen R. When each hexagon of a hexagonal system covers it. Discr. Appl. Math. 30 (1991) 63-75
23. Zhang F., and Zheng M. Generalized hexagonal systems with each hexagon being resonant. Discr. Appl. Math. 36 (1992) 67-73
24. H. Zhang, Perfect matchings in plane elementary bipartite graph, Ph.D. Thesis, Sichuan University, 1994.
25. Zhang H., Lam P.C.B., and Shiu W.C. Cell rotation graphs of strongly connected orientations of plane graphs with an application. Discr. Appl. Math. 130 (2003) 469-485
26. Zhang H., and Zhang F. The Clar covering polynomial of hexagonal systems I. Discr. Appl. Math. 69 (1996) 147-167
27. Zhang H., and Zhang F. Plane elementary bipartite graphs. Discr. Appl. Math. 105 (2000) 291-311