k-resonance in benzenoid systems, open-ended carbon nanotubes, toroidal polyhexes; and k-cycle resonant graphs

Match

Volumn 56, Issue 3, 2006, Pages 439-456

  Guo, Xiaofeng ^a  

^a XIAMEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846452164     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (53)

1. M. Randic, Chem. Phys. Lett. 38(1976)68.
2. I. Gutman and M. Randic, A correlation between Kekule valence structure and conjugated circuits, Chem. Phys. 41(1979)265-270.
3. M. Randic, J. Am. Chem. Soc. 99 (1977) 444.
4. M. Randic, Tetrahedron 33 (1977) 1905.
5. S. Nikolic, M. Randic, D. J. Klein, D. Plavsic and N. Trinajstic, J. Mol. Struct. 198 (1989) 223-237.
6. H. Vogler and N. Trinajstic, Theor. Chim. Acta 73 (1988) 437-448.
7. S. Nikolic, N. Trinajstic and D. J. Klein, Comput. Chem. 14 (1990) 313-322.
8. D. Plavsic, S. Nikolic and N. Trinajstic, J. Math. Chem. 8 (1991) 113-120.
9. D. Plavsic, S. Nikolic and N. Trinajstic, Croatica Chemica Acta 63 (1990) 683-692.
10. N. Trinajstic and S. Nikolic, J. Mol. Struct. (Theochem) 229 (1991) 63-89.
11. Xiaofeng Guo, M. Randic, Recursive Method for Enumeration of Linearly Independent and Minimal Conjugated Circuits of Benzenoid Hydrocarbons, J. Chem. Inf. Comput. Sci. 34 (1994) 339-348.
12. Xiaofeng Guo, M. Randic, and D.J.Klein, Analytical Expressions for the Count of LM-Conjugated Circuits of Benzenoid Hydrocarbons, International Journal of Quantum Chemistry 60 (1996) 943-958.
13. E. Clar, The Aromatic Sextet (Wiley, London, 1972).
14. H. Hosoya and T. Yamaguchi, Tetrahedron Lett. (1975) 4669.
15. N. Ohkami, A. Motoyama, T. Yamaguchi, H. Hosoya and I. Gutman, Tetrahedron 37 (1981) 1113.
16. I. Gutman, MATCH Commun. Math. Comput. Chem. 11 (1981) 127.
17. I. Gutman, Bull. Soc. Chim. Beograd 47 (1982) 453.
18. Fuji Zhang and Xiaofeng Guo, Directed Tree Structure of the Set of Kekule Patterns of Generalized Polyhex Graphs, Discrete Applied Mathematics 32 (1991) 295-302.
19. Xiaofeng Guo and Fuji Zhang, An Improvement of the Canonical P-V Path Elmination for Recognizing Kekulean Benzenoid systems, J. Mathematical Chemistry 9 (1992) 11-17.
20. Xiaofeng Guo and Fuji Zhang, Mathematical Properties and Structures of Sets of Sextet Patterns of Generalized Polyhexes, J. Mathematical Chemistry 9 (1992) 279-290.
21. Rongsi Chen, S. J. Cyvin and B. N. Cyvin, MATCH Commun. Math. Comput. Chem. 25 (1990) 71
22. Xueliang Li and Fuji Zhang, MATCH Commun. Math. Comput. Chem.25 (1990) 153.
23. Fuji Zhang and Xueliang Li, MATCH Commun. Math. Comput. Chem. 25 (1990) 251.
24. I. Gutman, Covering hexagonal system with hexagons, in: Graph Theory, Proceedings of the Fourth Yugoslav Seminar on Graph Theory, Novi Sad University, 1994, 151-160.
25. Fuji Zhang and Rongsi Chen, When each hexagon of a hexagonal system covers it, Discrete Appl. Math. 30 (1991) 63-75.
26. Fuji Zhang and Maolin Zheng, Generalized hexagonal systems with each hexagon being resonant, Discrete Applied Mathematics 36(1992)67-73.
27. Maolin Zheng, k-resonant benzenoid systems, J. Mol. Struct. (Theochem) 231 (1991) 321.
28. Fuji Zhang, Rongsi Chen, and Xiaofeng Guo, Hexagonal System Theory, in prepareing..
29. Rongsi Chen and Xiaofeng Guo, k-Coverable Coronoid Systems, J. Mathematical Chemistry 12(1993)147-162.
30. K. Lin and R. Chen, ARS Combinatoria 43 (1996) 33.
31. Fuji Zhang, Lusheng Wang, k-resonance of open-ended carbon nanotubes, Journal of Mathematical Chemistry Vol. 35, No. 2,2004, 87-103
32. Heping Zhang and Fuji Zhang, Plane elementary bipartite graphs, Discrete Appl. Math. 105 (2000) 291.
33. Wai Chee Shiu, Peter Che Bor Lam, Heping Zhang, k-resonance in toroidal polyhexes, Journal of Mathematical Chemistry Vol. 38, No. 4, 2005,451-466.
34. Xiaofeng Guo and Fuji Zhang, k-Cycle Resonance Graphs, Discrete Mathematics 135 (1994) 113-120.
35. Xiaofeng Guo, Fuji Zhang, Planar k-Cycle Resonant Graphs with k=1,2, Discrete Applied Mathematics 129 (2003) 383-397.
36. Zhixia Xu, Xiaofeng Guo, Construction and Recognition of Plamar One-Cycle Resonant Graphs, New York Academy of Sciences, Graph Theory Notes of New York XLII (2002) 44-48.
37. Biao Zhao, Xiaofeng Guo, Construction and Decomposition of Planar Two-Cycle Resonant Graphs, MATCH Commun. Math. Comput. Chem. 49 (2003) 83-98.
38. Biao Zhao, Xiaofeng Guo, A Linear Algorithm for Recognizing Planar Two-Cycle Resonant Graphs, MATCH Commun. Math. Comput. Chem. 50 (2004) 165-182.
39. Xiaofeng Guo, Fuji Zhang, Reducible Chains of Planar 1-Cycle Resonant Graphs, Discrete Mathematics 275 (2004) 151-164.
40. C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605.
41. D. Marusic and T. Pisanski, Symmetries of hexagonal molecular graphs on the torus, Croat. Chem. Acta 73 (4) (2000) 969.
42. Xiaofeng Guo, Fuji Zhang, k-Resonant Benzenoid Systems and k-Cycle Resonant Graphs, J. Chem. Inf. Comput. Sci. 41 (2001) 480-483.
43. L. Lovasz and M. D. Plummer, Matching Theory, Annals of Discrete Math. 29 (1986).
44. G. Hetyei, Rectangular configurations which can be covered by 2 x 1 rectangles, Pecsi Tan. Foisk. Kozl. 8 (1964) 351-367.
45. L. Lovasz, A note on factor-critical graphs, Studia Sci. Math. Hungar. 7 (1972) 279-280.
46. L. Lovasz, Ear-decompositions of matching-covered graphs, Combinatorica 2 (1983) 395-407.
47. L. Lovasz and M. D. Plummer, On bicritical graphs, Infinite and Finite Sets (Colloq. Keszthely, Hungary, 1973), II, Colloq. Math. Soc. Janos Bolyai 10 (1975) 1051-1079.
48. L. Lovasz and M. D. Plummer, On a family of planar bicritical graphs, Proc. London Math. Soc. Ser. (3) 30 (1975) 160-176.
49. L. Lovasz and M. D. Plummer, On minimal elementary bipartite graphs, J. Combin. Theory Ser. B 23 (1977) 127-138.
50. D. Naddef and W. R. Pulleyblank, Ear decompositions of elementary graphs and GF(2)-rank of perfect matchings, Am. Discrete Math. 16 (1982) 241-260.
51. M. D. Plummer, On n-extendable graphs, Discrete Math. 31 (1980) 201-210.
52. M. D. Plummer, Extending matchings in graphs: a survey, Discrete Math. 127 (1994) 277-292.
53. M. D. Plummer, Extending matchings in graphs: an update, Congr. Numer. 116 (1996) 3-32.