Perfect matchings in polyhexes, or recent graph-theoretical contributions to benzenoids

Journal of Universal Computer Science

Volumn 13, Issue 11, 2007, Pages 1514-1539

  Balaban, Alexandru T ^a   Randić, Milan ^b,c  

^a TEXAS A AND M UNIVERSITY AT GALVESTON   (United States)

^b NATIONAL INSTITUTE OF CHEMISTRY   (Slovenia)

^c DRAKE UNIVERSITY   (United States)

Author keywords

Clar structures; Isoarithmic benzenoids; Perfect matchings (1 factors, resonance structures, or Kekul structures); Polycyclic aromatic hydrocarbons (polyhexes or benzenoids)

Indexed keywords

EID: 38749148430     PISSN: 0958695X     EISSN: 09486968     Source Type: Journal    
DOI: None     Document Type: Article

References (57)

1. Bamberger, E.: Ber. dtsch. ehem. Ces. 24 (1891), 1758.
2. Bamberger, E.: Liebigs Ann. Chem. 273 (1893), 373.
3. Balaban, A. T.: "An attempt for the systeinatization of monocyclic aromatic compounds (Aromaticity I);. Studii si cercetari chim., Acad. R. P. Romania 7 (1959), 257-295. (in Romanian)
4. Balaban, A. T.: "Chemical graphs. VII. Proposed nomenclature of branched cata-condensed benzenoid polycyclic hydrocarbons": Tetrahedron 25 (1969), 2949-2956.
5. Balaban, A. T., Ed.: "Chemical Applications of Graph Theory"; Academic Press, London (1976).
6. Balaban, A. T.: "Is aromatieity outmoded?": Pure Appl. Chem. 52 (1980), 1409-1429:
7. Balaban, A. T.: "Chemical graphs. Part 50. Symmetry and enumeration of fibonacenes (unbranched catacondensed benzenoids isoarithmic with beliehnes and zigzag catafusenes)"; MATCH, Commun. Math. Comput. Chem. 24 (1989), 29-38.
8. Balaban, A. T., Harary, F.: "Chemical graphs. V. Enumeration and proposed nomenclature of benzenoid cata-condensed polycyclic aromatic hydrocarbons" Tetrahedron 24 (1968), 2505-2516.
9. Balaban, A.T., Randić, M.: "Partitioning of π-electrons in rings of polycyclic conjugated hydrocarbons. Part 2. Coronoids"; J. Chem. Inf. Comput. Sci. 44 (2004), 50-59.
10. Balaban, A.T., Randić, M.: "Partitioning of π-electrons in rings of polycyclic conjugated hydrocarbons. Part 3. Perifusenes"; New J. Chem. 28 (2004), 800-806.
11. Balaban, A.T., Randić, M.: "Partitioning of π-electrons in rings of polycyclic conjugated hydrocarbons. Part 5. Non-alternant hydrocarbons"; J. Chem. Inf. Comput. Sci. 44 (2004), 1701-1707.
12. Balaban, A.T., Randić, M.: "Partitioning of π-electrons in rings of polycyclic conjugated hydrocarbons. Part 6. Comparison with other methods for estimating the local aromaticity of rings in polycyclic benzenoids"; J. Math. Chem. 37 (2005), 443-453.
13. Balaban, A. T., Tomescu, I: "Algebraic expressions for the number of Kekulé structures of isoarithmic cata-condensed polycyclic hydrocarbons"; MATCH, Commun. Math. Comput. Chem. 14 (1983), 155-182.
14. |Balaban and Tomescu 1984] Balaban, A. T., Tomescu, I.: "Chemical graphs. XL. Three relations between the Fibonacci sequence and the numbers of Kekulé structures for non-branched cata-condensed polycvclic aromatic hydrocarbons"; Croatia Chem. Acta, 57 (1984), 391-404.
15. Balaban, A. T., Tomescu, I.: "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.
16. Balaban, A. T., Tomescu, I.: "Alternating 6-cycles in perfect matchings of graphs representing condensed benzenoid hydrocarbons"; Discrete Appl. Math., 19 (1988), 16. Reprinted in "Application of Graphs in Chemistry and Physics" (J. W. Kennedy and L. W. Quintas, editors), North-Holland, Amsterdam, 1988, p. 5-16.
17. Tomescu, I., Balaban, A. T.: "Decomposition theorems for calculating the number of Kekulé structures in coronoids fused via perinaphthyl units". MATCH, Commun. Math. Comput. Chem. 1989, 24, 289-389:
18. Balaban, A.T., Banciu, M., Ciorba, V.: "Annulenes, Benzo-, Helero-, Homo-Derivatives and Their Valence Isomers, Vol. 1"; ORC Press, Boca, Raton, Florida (1986).
19. Balaban, A. T., Artemi, C., Tomescu, I.: "Algebraic expressions for Kekulé structure counts in non-branched regularly cata-condensed benzenoid hydrocarbons"; MATCH, Commun. Math. Comput. Chem. 22 (1987), 77-100.
20. Biggs, N. L., Lloyd, E. K., Wilson, R .J.: "Graph Theory 1736 1936"; Reprinted edition with corrections, Clarendon, Oxford, 1977.
21. Boudy, J.A., MuHy, U.S.R.: "Graph Theory with Applications"; Elsevier North-Holland, Amsterdam, 1976.
22. Borinan, S.: "19th-century chemist Kekulé charged with scientific misconduct"; Chem. Eng. News 1993, August 23, 20-21.
23. Clar, E., "The Aromatic Sextet"; Wiley, London 1972.
24. Erlenmeyer, Liebigs E.: Ann. Chem. 137 (1866), 327.
25. Gutman, I., Randić, M.: "A correlation between Kekulé valence structures and conjugated circuits"; Chem. Phys. 41 (1979), 265-270.
26. Gutman, I., Turković, N., Jovicić, J.: "Cyclic conjugation in benzo-annelated perylenes. How empty is the empty ring?"; Monatsh. Chem. 135 (2004), 1389-1394.
27. Gutman, I., Vukičević, D., Graovac, A., Randić, M.: "Algebraic Kekulé structures of benzenoid hydrocarbons": J. Chem. Inf. Comput, Sci. 44 (2004), 296-299.
28. Gutman, I., Balaban, A. T., Randić, M., Kiss-Toth, C.Z.: "Partitioning of π-electrons in rings of fibonacenes"; Z. Naturforseh. 60a (2005), 171-176.
29. Harary, F.: "Graph Theory"; Addison-Wesley, Reading, MA, 1969.
30. Honsberger, R. (Ed.): "Mathematical Plums"; The Dolciani Math. Expositions, # 4; The Math. Assoc. Amer. 1979.
31. Kekulé, A.: "Sur la constitution des substances aromatiques"; Bull. Soc. Chim. Fr. 3 (1865), 98-110.
32. Kekulé, A.: "Untersuchungen ber aromatische Verbindungen"; Liebigs Ann. Chem. 137 (1866), 129-136.
33. It was at that conference on the 25th anniversary celebration of Kekulés benzene theory, held in Berlin City Hall in 1890 that A. Kekulé presented a lecture at which he first time mention dreaming of a snake biting its tail that gave him the idea of ring structure for benzene.
34. Klein, D. J., Randić, M.: "Innate degree of freedom of a graph"; J. Comput. Chem. 8 (1987), 516-521.
35. König, D.: "Theorie der endlichen und unendlichen Graphen"; Chelsea, 1935 (reprint of original published in 1935).
36. Ore, O.: "Theory of Graphs": AMS Colloquium Publications 38. Am. Math. Soc., 1962.
37. Pauling, L.: "The Nature of the Chemical Bond"; Cornell Univ. Press: Ithaca 1939.
38. Pauling, L., Wheland, G.: "The nature of the chemical bond. V. The quantum mechanical calculation of the resonance energy of benzene and naphthalene and the hydrocarbon free radicals": J. Chem. Phys. 1 (1933), 362-374.
39. Pauling, L., Brockway, L. O., Beach, J. Y.: "Dependence of interatomic distance on the single bond double bond resonance": J. Amer. Chem. Soc. 57 (1935), 2705-2709.
40. Randić, M.: "Conjugated circuits and resonance energies of benzenoid hydrocarbons"; Chem. Phys. Lett. 38 (1976), 68-70.
41. |Randić 1977a] Randić, M.: "Aromaticily and conjugation"; J. Am. Chem. Soc. 99 (1977), 444-450.
42. Randić, M.: "A graph theoretical approach to conjugation and resonance energies of hydrocarbons" ; Tetrahedron, 33 (1977), 1905-1920.
43. Randić, M.: "Clare π-Aromatic Sextet Revisited"; Chapter 16 in: Valence Bond Theory, (Cooper, D. L. Ed.), Elsevier, Amsterdam (2002), 503-533.
44. Randić, M.: "Quantum Chemical Justification for Clar Valence Structures; (Festschrift for Professor R. G. Parr) Reviews of Modern Quantum Chemistry, vol. 1, K. D. Sen, Ed., World Scientific: Singapore (2002) 204-239.
45. Randić, M.: "Aromaticity of polycyclic conjugated hydrocarbons"; Chem. Rev. 103 (2004), 3449-3605.
46. Randić, M.: "Algebraic Kekulé formulas for benzenoid hydrocarbons"; J. Chem. Inf. Comput. Sci. 44 (2004), 365-372.
47. Randić, M., Balaban, A. T.: "Partitioning of π-electrons in rings of polycyclic hydrocarbons. Part 1. Catacondensed benzenoids"; Polycyclic Arom. Comp. 24 (2004), 173-193.
48. Randić, M., Balaban, A. T.: "Partitioning of π-electrons in rings for Clar structures of benzenoid hydrocarbons" ; J. Chem, Inf. Model. 46 (2006), 57-64.
49. Randić, M., Balaban, A. T.: "Ring signatures for benzenoids with up to seven rings. Part 1, cata-Gondensed systems"; Submitted for publication.
50. Balaban, A. T., Randić, M.: "Ring signatures for benzenoids with up to seven rings. Part 2. peri-Condensed systems" ; Submitted for publication.
51. Randić, M., Klein, D. J.: "Kekulé valence structures revisited. Innate degree of freedom of π-electron coupling" ; In: Mathematical and Computational Concepts in Chemistry, Trinajstić, N. Ed., Ellis Horwood: New York (1985) 274-282.
52. Ringsfield, N., Ringel, G.: "Pearls in Graph Theory: A Comprehensive Introduction"; Academic Press, London, 1990, 1994; Dover Publ. Inc., Mineola, NT, 1994.
53. Sedlar, J., Andelić, I., Gutman, I., Graovac, A.: "Vindicating the Pauling bond-order concept"; Chem. Phys. Lett. 427 (2006), 418-420.
54. Sylvester, J. J.: "Chemistry and algebra"; Nature 17 (1878) 284-309.
55. Vukičević, D., Randić, M., Balaban, A. T.: "Partitioning of Trelectrons in rings of polycyclic conjugated hydrocarbons. Part 4, Benzenoids with more than one geometric Kekulé structure corresponding to the same algebraic Kekulé structure"; J. Math. Chem. 36 (2004), 271-279.
56. Wheland, G. W.: "Resonance in Organic Chemistry"; Wiley, New York, 1955.
57. Wilson, R. J.: "Introduction to Graph Theory"; Oliver and Boyd, Edinburgh, 1972;