Zhang-Zhang polynomials of cyclo-polyphenacenes

Journal of Mathematical Chemistry

Volumn 46, Issue 2, 2009, Pages 347-362

  Guo, Qiuzhi ^a   Deng, Hanyuan ^a   Chen, Dandan ^a  

^a HUNAN NORMAL UNIVERSITY   (China)

Author keywords

Clar covering polynomial; Clar number; Cyclo polyphenacene; Herndon number; Kekul structure; Zhang Zhang polynomial

Indexed keywords

EID: 67650631662     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-008-9466-4     Document Type: Article

References (33)

1. Cyvin S.J., Gutman I.: Kekulé Structures in Benzenoid Hydrocarbons, Lecture Notes in Chemistry, vol. 46. Springer, Berlin (1988)
2. Gutman I., Cyvin S.J.: Introduction to the Theory of Benzenoid Hydrocarbons. Springer, Berlin (1989)
3. I. Gutman, S.J. Cyvin (eds.), Advance in the Theory of Benzenoid Hydrocarbons, Topics Curr. Chem. 153 (Springer, Berlin, 1990)
4. Clar E.: The Aromatic Sextet. Wiley, New York (1972)
5. I. Gutman B. Furtula A.T. Balaban 2006 Algorithm for simultaneous calculation of Kekule and Clar structure counts, and Clar number of benzenoid molecules Polyc. Arom. Comp. 26 17 35 (Pubitemid 43259308)
6. S. El-Basil M. Randić 1988 Clar valence structures of benzenoid hydrocarbons J. Chem. Soc. Faraday Trans. 2 84 1875 1887
7. M. Randić S. El-Basil 1994 Graph theoretical analysis of large benzenoid hydrocarbons J. Mol. Struct. (Theochem) 304 233 245
8. M. Randić S. El-Basil S. Nikolić N. Trinajstić 1998 Clar polynomials of large benzenoid hydrocarbons J. Chem. Inf. Comput. Sci. 38 563 574 (Pubitemid 128571184)
9. H. Hosoya T. Yamaguchi 1975 Sextet polynomial: A new enumeration and proof technique for the resonance theory applied to the aromatic hydrocarbons Tetrohedron Lett. 52 4659 4662
10. H. Zhang F. Zhang 1996 The Clar covering polynomial of hexagonal systems I Discrete Appl. Math. 69 147 167 (Pubitemid 126392465)
11. H. Zhang F. Zhang 2000 The Clar covering polynomial of hexagonal systems III Discrete Math. 212 261 269
12. H. Zhang 1997 The Clar covering polynomial of hexagonal systems with an application to chromatic polynomials Discrete Math. 172 1-3 163 173 (Pubitemid 127392276)
13. I. Gutman S. Gojak B. Furtula 2005 Clar theory and resonance energy Chem. Phys. Lett. 413 396 399 (Pubitemid 41285252)
14. H. Zhang 1993 The Clar covering polynomial of S,T-isomers MATCH Commun. Math. Comput. Chem. 29 189 197
15. I. Gutman S. Gojak S. Stanković B. Furtula 2005 A concealed difference between the structure-dependence of Dewar and topological resonance energy J. Mol. Struct. (Theochem) 757 119 123
16. S. Gojak S. Radenković R. Kovačević S. Stankovic J. Durdević I. Gutman 2006 A difference between the pi-electron properties of catafusenes and perifusenes Polyc. Arom. Comp. 26 197 206 (Pubitemid 44034628)
17. I. Gutman S. Gojak B. Furtula S. Radenković A. Vodopivec 2006 Relating total π-electron energy and resonance energy of benzenoid molecules with Kekule- and Clar-structure-based parameters Monatsh. Chem. 137 1127 1138 (Pubitemid 44386681)
18. S. Gojak I. Gutman S. Radenković A. Vodopivec 2007 Relating resonance energy with Zhang-Zhang polynomial J. Serb. Chem. Soc. 72 673 679
19. I. Gutman B. Borouićanin 2006 Zhang-Zhang polynomial of multiple linear hexagonal chains Z. Naturforsch. 61a 73 77
20. S. Zhou H. Zhang I. Gutman 2008 Relations between Clar structures, Clar covers, and the sextet-rotation tree of a hexagonal system Discrete Appl. Math. 156 1809 1821
21. S. Iijima 1991 Helical microtubules of graphitic carbon Nature 354 56 58 (Pubitemid 21896780)
22. D.J. Klein W.A. Seitz T.G. Schmalzand 1993 Symmetry of infinite tubular polymers: application to buckytubes J. Phys. Chem. 97 1231 1236
23. D.J. Klein H. Zhu 1996 Resonance in elemental benzenoids Discrete Appl. Math. 67 157 173 (Pubitemid 126369797)
24. H. Sachs P. Hansen M. Zheng 1996 Kekule count in tubular hydrocarbons MATCH Commun. Math. Comput. Chem. 33 169 241 (Pubitemid 126325664)
25. J.Cz. Dobrowolsky 2002 On the belt and Moebius isomers of the coronene molecule J. Chem. Inf. Comput. Sci. 42 490 499
26. K.N. Hook P.S. Lee M. Nendel 2001 Polyacene and cyclacene geometries and electronic structures: bond equalization, vanishing band gaps, and triplet ground states contrast with polyacetylene J. Org. Chem. 66 5517 5521 (Pubitemid 32878905)
27. H.S. Choi K.S. Kim 1999 Structures, magnetic properties, and aromaticity of cyclacenes Angew. Chem. Int. Ed. 38 15 2256 2258 (Pubitemid 29391868)
28. L. Turker 2000 Borazine embedded cyclacenesa theoretical study J. Mol. Struct. (THEOCHEM) 531 401 405
29. A. Misra D.J. Klein 2002 Characterization of cyclo-polyphenacenes J. Chem. Inf. Comput. Sci. 42 1171 1175 (Pubitemid 35360301)
30. L. Wang F. Zhang H. Zhao 2005 On the ordering of benzenoid chains and cyclo-polyphenacenes with respect to their numbers of Clar aromatic sextets J. Math. Chem. 38 293 309 (Pubitemid 41167756)
31. I. Gutman, S.J. Cyvin (eds.), Advance in the Theory of Benzenoid Hydrocarbons, Topics Curr. Chem. 153 (Springer, Berlin, 1990)
32. W.C. Herndon 1974 Thermochemical parameters for benzenoid hydrocarbons Thermochim. Acta 8 225 237
33. N. Trinajstić, Chemical Graph Theory, 2nd edn. (CRC Press, 1992)