A comparison between 1-factor count and resonant pattern count in plane non-bipartite graphs

Journal of Mathematical Chemistry

Volumn 38, Issue 3, 2005, Pages 315-324

  Zhang, Heping ^a   He, Jinghua ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

Benzenoid; Fullerene; Kekul structure; Plane graph; Resonant pattern

Indexed keywords

EID: 25144447546     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-005-5821-x     Document Type: Article

References (22)

1. J. Aihara 1977 Aromatic sextets and aromaticity in benzenoid hydrocarbons Bull. Chem. Soc. Jpn. 50 2010
2. 60. Kekulé counts versus stability Chem. Phys. Lett. 228 478
3. W.E. Barth R.G. Lawton 1971 The synthesis of corannulen J. Am Chem. Soc. 93 1730
4. J.L. Bergan B.N. Cyvin S.J. Cyvin 1987 The Fibonacci numbers, and Kekulé structures of some corona-condensed benzenoids (corannulenes) Acta Chim Hung. 124 299
5. E. Clar 1972 The Aromatic Sextet Wiley London
6. 60 using the Heisenberg model J. Chem. Phys. 109 3 873
7. P.W. Fowler D.E. Manolopoulos 1995 An Atlas of Fullerenes Clarendon Press Oxford
8. I. Gutman 1981 The R-polynomial: a new combinatorial technique in resonance theory Bull. Soc. Chim. Beograd 46 17
9. I. Gutman S.J. Cyvin 1989 Introduction to the Theory of Benzenoid Hydrocarbons Springer Berlin
10. W.C. Herndon 1973 Resonance energies of aromatic hydrocarbons: a quantitative test of resonance theory J. Am. Chem. Soc. 95 2404
11. Hosoya H., Yamaguchi T. Sextet polynomial. A new enumeration and proof technique for the resonance theory applied to the aromatic hydrocarbons Tetrahedron Lett. (1975) 4659
12. P.E. John 1994 Calculating the cell polynomial of catacondensed polycyclic hydrocarbons J. Chem. Inform. Comput. Sci. 34 357
13. P.E. John H. Sachs M. Zheng 1995 Kekulé patterns and Clar patterns in bipartite plane graphs J. Chem. Inform. Comput. Sci 35 1019
14. 60: Buckminsterfullerene Nature 318 162
15. N. Ohkami A. Motoyama T. Yamaguchi H. Hosoya I. Gutman 1981 Graph-theoretical analysis of the Clar's aromatic sextet Tetrahedron. 37 1113
16. M. Randć 1976 Conjugated circuits and resonance energies of benzenoid hydrocarbons Chem. Phys. Lett. 38 68
17. M. Randć 2003 Aromaticity of polycyclic conjugated hydrocarbons Chem. Rev. 103 3449
18. 60 carbon cages Chem. Phys. Lett. 130 203
19. W.C. Shiu P.C.B Lam F. Zhang H. Zhang 2002 Normal components, Kekulé patterns, and Clar patterns in plane bipartite graphs J. Math. Chem. 31 405
20. W.C. Shiu P.C.B. Lam H. Zhang 2003 Clar and sextet polynomials of buckministerfullerene J. Mol. Struct. (Theochem) 662 3 239
21. F. Zhang R. Chen 1986 A theorem concerning polyhex graphs MATCH Commun. Math. Comput. Chem 19 179
22. H. Zhang F. Zhang 2001 New lower bound on the number of perfect matchings of fullerene graphs J. Math. Chem. 30 3 343