A linear algorithm for recognizing planar two-cycle resonant graphs

Match

Volumn , Issue 50, 2004, Pages 165-182

  Zhao, Biao ^a   Guo, Xiaofeng ^a,b  

^a XINJIANG UNIVERSITY   (China)

^b XIAMEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; MATHEMATICAL COMPUTING; MATHEMATICS;

EID: 12444279979     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (41)

1. L. Pauling, The calculation of matrix elements for Lewis electronic structures of molecules, J. Chem. Phys. 1 (1933) 280-283.
2. L. Pauling and G. W. Wheland, The nature of the chemical bond. V. The quantum-mechanical calculation of the resonance energy of benzene and naphtalene and the hydrocarbon free radicals, J. Chem. Phys. 1 (1933) 362-374.
3. L. Pauling, J. Sherman, The nature of the chemical bond. VI. The calculation from thermochemical data of the energy of resonance of molecules among several electronic structures, J. Chem. Phys. 1 (1933) 606-617.
4. L. Pauling, G. W. Wheland, The nature of the chemical bond. V. (erratum), J. Chem. Phys. 2 (1934) 482-482
5. W. C. Herndon, Structure-resonance theory - A review of applications to π-hydrocarbon systems, Isr. J. Chem. 20 (1980) 270.
6. W. T. Simpson, On the use of structures as an aid in understanding π-electron spectra, J. Am. Chem. Soc. 75 (1953) 593.
7. W. C. Herndon, Resonance energies of aromatic hydrocarbons. A quantitative test of resonance theory, J. Am. Chem. Soc. J. Am. Chem. Soc. 95 (1973) 2404-2406.
8. W. C. Herndon, Thermochemical parameter for benzenoid hydrocarbons, Thermochim Acta 8 (1974) 225-237.
9. I. Gutman, W. C. Herndon, On resonance theory, Chem. Phys. Lett. 34 (1975) 387-391.
10. M. Randić, Conjugated circuits and resonance energies of benzenoid hydrocarbons. Chem. Phys. Lett. 38 (1976) 68-70.
11. I. Gutman and M. Randić, A correlation between Kekulé valence structures and conjugated circuits, Chem. Phys. 41 (1979) 265-270.
12. M. Randić, Aromaticity and conjugation, J. Am. Chem. Soc. 99 (1977) 444-450.
13. M. Randić, A graph theoretical approach to conjugation and resonance energies of hydrocarbons, Tetrahedron 33 (1977) 1905-1920.
14. D. J. Klein and N. Trinajstić, Foundations of conjugated-circuit models, Pure Appl. Chem. 61 (1989) 2107-2115.
15. D. J. Klein, Semiempirical valence bond views for benzenoid hydrocarbons, Topics Curr.Chem. 153 (1990) 57-83.
16. N. Trinajstić, Chemical Graph Theory, CRC Press Inc. 1992.
17. S. Nikolić, M. Randić, D. J. Klein, D. Plavsic and N. Trinajstic, The conjugated circuit model: Application to benzenoid hydrocarbons, J. Mol. Struct. 198 (1989) 223-237.
18. H. Vogler and N. Trinajstić, The conjugated circuit model. On the geometries of annelated [n] annulenes, Theor. Chim. Acta 73 (1988) 437-448.
19. S. Nikolić, N. Trinajstić and D. J. Klein, The conjugated-circuit model, Comput. Chem. 14 (1990) 313-322.
20. D. Plavsic, S. Nikolić and N. Trinajstić, The conjugated-circuit model: The optimum parameters for benzenoid hydrocarbons, J. Math. Chem. 8 (1991) 113-120.
21. D. Plavsic, S. Nikolić and N. Trinajstić, The conjugated-circuts model: On the selection of the parameters Croat. Chem. Acta 63 (1990) 683-692.
22. N. Trinajstić and S. Nikolić, Quantum mechanical and computational aspects of the conjugated-circuit model, J. Mol. Struct. (Theochem) 229 (1991) 63-89.
23. Guo Xiaofeng and 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.
24. Guo Xiaofeng, M. Randić, and D.J.Klein, Analytical expressions for the count of LM-conjugated circuits of benzenoid hydrocarbons, Int. J. Quantum Chem. 60 (1996) 943-958.
25. E. Clar, The Aromatic Sextet (Wiley, London, 1972).
26. H. Hosoya and T. Yamaguchi, Sextet polynomial. A new enumeration and proof techniquefor the resonance theory applied to the artomatic hydrcarbons, Tetrahedron Lett. (1975) 4662-4669.
27. N. Ohkami, A. Motoyama, T. Yamaguchi, H. Hosoya and I. Gutman, Graph-theoretical analysis of the Clar's aromatic sextet, Tetrahedron 37 (1981) 1113-1122.
28. I. Gutman, Some combinatorial consequences of Clar's resonant sextet theory, MATCH - Commun. Math. Comput. Chem. 11 (1981) 127-143.
29. I. Gutman, Topological properties of benzenoid molecules, Bull. Soc. Chim. Beograd 47 (1982) 453.
30. Zhang Fuji and Guo Xiaofeng, Directed tree structure of the set of Kekulé patterns of generalized polyhex graphs, Discrete Appl. Math. 32 (1991) 295-302.
31. Guo Xiaofeng and Zhang Fuji, An improvement of the canonical p-v path elmination for recognizing Kekulean benzenoid systems, J. Math. Chem. 9 (1992) 11-17.
32. Guo Xiaofeng and Zhang Fuji, Mathematical properties and structures of sets of sextet patterns of generalized polyhexes, J. Math. Chem. 9 (1992) 279-290.
33. Chen Rongsi, S. J. Cyvin and B. N. Cyvin, Recognition of essentially disconnected benzenoids, MATCH - Commun. Math. Comput. Chem. 25 (1990) 71-81.
34. Li Xueliang and Zhang Fuji, A fast algorithm to determine fixed bonds in hexagonal systems, MATCH - Commun. Math. Comput. Chem. 25 (1990) 151-163.
35. Zhang Fuji and Li Xueliang, Hexagonal systems without fixed double bonds, MATCH - Commun. Math. Comput. Chem. 25 (1990) 251-259.
36. Xiaofeng Guo and Fuji Zhang, k-cycle resonant graph, Discrete Math. 135 (1994) 113-120.
37. Guo Xiaofeng, Zhang Fuji, Planar k-Cycle resonant graphs with k=1,2, Discrete Applied Mathematics, to appear.
38. Zhixia Xu and Xiaofeng Guo, Construction and recognition of planar one-cycle resonant graphs, Graph Theory Notes New York XLII, 44-48 (2002).
39. Biao Zhao and Xiaofeng Guo, Construction and decompsition of planar two-cycle resonant graphs, MATCH - Commun. Math. Comput. Chem., to appear.
40. J.A.Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillian, London and Elsevier, New York, 1976.
41. L. Lovász and M. D. Plummer, Matching Theory, Ann. Discrete Math. 29 (1986).