Zhang-Zhang polynomials of various classes of benzenoid systems

Match

Volumn 68, Issue 1, 2012, Pages 31-64

  Chou, Chien Pin ^a   Li, Yenting ^a   Witek, Henryk A ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

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EID: 84898731937     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. C. P. Chou, H.A. Witek, An algorithm and FORTRAN program for automatic computation of the Zhang-Zhang polynomial of benzenoids, MATCH Commun. Math. Comput. Chem. 68 (2012) 3-30.
2. H. P. Zhang, F. J. Zhang, The Clar covering polynomial of hexagonal systems. 1. Discr. Appl. Math. 69 (1996) 147-167.
3. F. J. Zhang, H. P. Zhang, Y. T. Liu, The Clar covering polynomial of hexagonal systems. 2. An application to resonance energy of condensed aromatic hydrocarbons, Chin. J. Chem. 14 (1996) 321-325.
4. H. P. Zhang, The Clar covering polynomial of hexagonal systems with an application to chromatic polynomials, Discr. Math. 172 (1997) 163-173.
5. H. P. Zhang, F. J. Zhang, The Clar covering polynomial of hexagonal systems III, Discr. Math. 212 (2000) 261-269.
6. I. Gutman, S. Gojak, B. Furtula, Clar theory and resonance energy, Chem. Phys. Lett. 413 (2005) 396-399. (Pubitemid 41285252)
7. I. Gutman, B. Furtula, A. Balaban, Algorithm for simultaneous calculation of Kekulé and Clar structure counts, and Clar number of benzenoid molecules, Polyc. Aromat. Comp. 26 (2006) 17-35. (Pubitemid 43259308)
8. I. Gutman, S. Gojak, B. Furtula, S. Radenković, A. Vodopivec, Relating total π-electron energy and resonance energy of benzenoid molecules with Kekulé- and Clar-structure-based parameters, Monatsh. Chem. 137 (2006) 1127-1138. (Pubitemid 44386681)
9. I. Gutman, B. Borovićanin, Zhang-Zhang polynomial of multiple linear hexagonal chains, Z. Naturforsch. 61a (2006) 73-77. (Pubitemid 43734082)
10. S. Gojak, S. Stankovic, I. Gutman, B. Furtula, Zhang-Zhang polynomial and some of its applications, in: I. Gutman (Ed.), Mathematical Methods in Chemistry, Prijepolje Museum, Prijepolje, 2006, pp. 141-158.
11. S. Gojak, I. Gutman, S. Radenković, A. Vodopivec, Relating resonance energy with the Zhang-Zhang polynomial. J. Serb. Chem. Soc. 72 (2007) 673-679.
12. S. Zhou, H. Zhang, I. Gutman, Relations between Clar structures, Clar covers, and the sextet-rotation tree of a hexagonal system, Discr. Appl. Math. 156 (2008) 1809-1821.
13. D. Chen, H. Deng, Q. Guo, Zhang-Zhang polynomials of a class of pericondensed benzenoid graphs, MATCH Commun. Math. Comput. Chem. 63 (2010) 401-410.
14. H. Zhang, N. Ji, H. Yeo, Transfer-matrix calculation of the Clar covering polynomial of hexagonal systems, MATCH Commun. Math. Comput. Chem. 63 (2010) 379-392.
15. E. Clar, The Aromatic Sextet, Wiley, London, 1972.
16. S. J. Cyvin, I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
17. M. B. Monagan, W. M. Software, Maple V programming guide, Springer, Berlin, 1998.
18. A. T. Balaban, I. Tomescu, Chemical graphs. XLI. Numbers of conjugated circuits and Kekulé structures for zigzag catafusenes and (J, K)-hexes; generalized fibonacci numbers, MATCH Commun. Math. Comput. Chem. 17 (1985) 91-120.
19. D. Biermann, W. Schmidt, Diels-Alder reactivity of polycyclic aromatic-hydrocarbons. 3. New experimental and theoretical results, Isr. J. Chem. 20 (1980) 312-318.
20. Y. S. Jiang, Graph theory of molecular orbitals - calculation of an - the determinant of adjacency matrix and the stability of moleculesmolecules, Sci. Sin. 23 (1980) 847-861.
21. Q. Z. Guo, H. Y. Deng, D. Chen, Zhang-Zhang polynomials of cyclo-polyphenacenes, J. Math. Chem. 46 (2009) 347-362.
22. C. P. Chou, H. A. Witek, Comment on "Zhang-Zhang polynomials of cyclo-polyphenacenes" by Q. Guo, H. Deng, D. Chen, J. Math. Chem. submitted.
23. M. Gordon, W. H. T. Davison, Theory of resonance topology of fully aromatic hydrocarbons. I, J. Chem. Phys. 20 (1952) 428-435.
24. S. J. Cyvin, B. N. Cyvin, I. Gutman, Number of Kekulé structures of 5-tier strips, Z. Naturforsch. 40a (1985) 1253-1261.
25. S. J. Cyvin, The number of Kekulé structures of hexagon-shaped benzenoids and members of other related classes, Monatsh. Chem. 117 (1986) 33-45.
26. S. J. Cyvin, Enumeration of Kekulé structures - Chevrons, J. Mol. Struct. (Theochem) 26 (1985) 211-219.
27. S. J. Cyvin, I. Gutman, Kekulé structures and their symmetry properties, Comput. Math. Appl. B. 12 (1986) 859-876.
28. N. Ohkami, H. Hosoya, Topological dependency of the aromatic sextets in polycyclic benzenoid hydrocarbons - Recursive relations of the sextet polynomial, Theor. Chim. Acta. 64 (1983) 153-170.
29. I. Gutman, S. J. Cyvin, Topological properties of benzenoid systems. 35. Number of Kekulé structures of multiple-chain aromatics, Monatsh. Chem. 118 (1987) 541-552.
30. S. J. Cyvin, I. Gutman, Topological properties of benzenoid systems. Part XXXVI. Algorithm for the number of Kekulé structures in some peri-condensed benzenoids, MATCH Commun. Math. Comput. Chem. 19 (1986) 229-242.
31. T. F. Yen, Resonance topology of polynuclear aromatic hydrocarbons, Theor. Chim. Acta. 20 (1971) 399-404.