A survey and new results on computer enumeration of polyhex and fusene hydrocarbons

Journal of Chemical Information and Computer Sciences

Volumn 43, Issue 3, 2003, Pages 842-851

  Brinkmann, Gunnar ^a   Caporossi, Gilles ^b   Hansen, Pierre ^b  

^a BIELEFELD UNIVERSITY   (Germany)

^b GERAD   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; GRAPH THEORY; ISOMERS; MOLECULAR STRUCTURE;

COMPUTER ENUMERATION;

HYDROCARBONS;

EID: 0037498087     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci025526c     Document Type: Review

References (40)

1. Balaban, A. T.; Brunvoll, J.; Ciolowski, J.; Cyvin, B. N.; Cyvin, S. J.; Gutman, I.; He, W. J.; Knop, J. V.; Kovacevie, M.; Müller, W. R.; Szymanski, K.; Tosić, R.; Trinajstić, N. Enumeration of benzenoid and coronoid hydrocarbons, Z. Naturforsch. 1987, 42a, 863-870.
2. Dias, J. R. Benzenoid hydrocarbons. In Handbook of Polycyclic Hydrocarbons; Elsevier: Amsterdam, 1987.
3. Gutman, I.; Cyvin, S. J. Introduction to the Theory of Benzenoid Hydrocarbons; Springer-Verlag: 1989.
4. Balaban, A. T. Enumeration of isomers. In Chemical Graph theory; Abacus Press, Gordon and Breach: New York, 1990; pp 177-234.
5. Balasubramanian, K. Recent chemical applications of computational combinatorics and graph theory. In Computational Chemical Graph Theory; Rouvray, D. H., Ed.; Nova Science: New York, 1990.
6. Hosoya, H. Some recent advances in counting polynomials in chemical graph theory. In Computational Chemical Graph Theory: Rouvray, D. H., Ed.; Nova Science: New York, 1990.
7. Knop, J. V.; Müller, W. R.; Szymanski, K. Computer-oriented molecular codes. In Computational Chemical Graph Theory; Rouvray, D. H., Ed.; Nova Science: New York, 1990.
8. Mercier, C.; Sobel Y.; Dubois J.-E. Darc/pelco method: A topological tool for qsar search and its reliable predictive capability. In Chemical Graph theory; Abacus Press, Gordon and Breach: New York, 1990; pp 199-258.
9. Trinajstić, N.; Nikolić, S.; Knop, J. V.; Müller, W. R.; Szymanski, K. Computational Chemical Graph Theory; Ellis Horwood: 1991.
10. Bonchev, D.; Rouvray, D. H. Chemical Graph Theory, Introduction and Fundamentals; Abacus Press, Gordon and Breach: New York, 1991.
11. Bonchev, D.; Rouvray, D. H. Chemical Graph Theory, reactivity and Kinetics; Abacus Press, Gordon and Breach: New York, 1992.
12. Brunvoll, J. Cyvin, B. N.; Cyvin, S. J. Enumeration of benzenoid systems and other polyhexes. Topics Curr. Chem. 1992, 162, 65-180.
13. Vöge, M.; Guttmann, A. J.; Jensen, I. On the number of benzenoid hydrocarbons. Submitted for publication.
14. Knop, J. V.; Müller, W. R.; Szymanski, K.; Trinajstić, N. Use of small computers for large computations: Enumeration of polyhex hydrocarbons. J. Chem. Inf. Comput. Sci. 1990, 30, 159-160.
15. Tosić, R.; Masulović, D.; Stojmenović, I.; Brunvoll, J.; Cyvin, S. J. Cyvin, B. J. Enumeration of Polyhex Hydrocarbons to h = 17. J. Chem. Inf. Comput. Sci. 1995, 35, 181-187.
16. Cyvin, B. N.; Xiaofeng, G.; Cyvin, S. J.; Zhang, F. Enumeration of helicenes. Chem. Phys. Lett. 1992, 188, 537-542.
17. Knop, J. V.; Szymanski, K.; Jericević, Z.; Trinajstić, N. Computer enumeration and generation of benzenoid hydrocarbons and identification of bay regions. J. Comput. Chem. 1983, 4, 23-32.
18. Stojmenović, I.; Tosić, R.; Doroslovacki, R. Generating and Counting Hexagonal Systems. In Graph Theory, Proceedings of the sixth Yugoslav Seminar on Graph Theory; 1985.
19. He, W. J.; He, W. C.; Wang, Q. X.; Brunvoll, J.; Cyvin, S. J. Supplement to Enumeration of Benzenoid and Coronoid Hydrocarbons. Z. Naturforsch. 1988, 43a, 693-694.
20. Müller, W. R.; Szymanski, K.; Knop, J. V. On counting polyhex hydrocarbons. Croat. Chem. Acta 1989, 62, 481-483.
21. Nikolić, S.; Trinajstić, N.; Knop, J. V.; Müller, W. R.; Szymanski, K. On the concept of the weighted spanning tree of dualist. J. Math. Chem. 1990, 4, 357-375.
22. Balasubramanian, K.; Kaufman, J. J.; Koski, W. S.; Balaban, A. T. Graph theoretical characterisation and computer generation of certain carcinogenic benzenoid hydrocarbons and identification of bay regions. J. Comput. Chem. 1980, 1, 149-157.
23. Müller, W. R.; Szymanski, K.; Knop, J. V.; Nikolić, S.; Trinajstić, N. On the enumeration and generation of polyhex hydrocarbons. J. Comput. Chem. 1990, 11, 223-235.
24. Nikolić, S.; Trinajstić, N.; Knop, J.; Müller, W. R.; Szymanski, K. On the classification and enumeration of planar polyhex hydrocarbons. J. Mol. Struct. (Theochem.) 1991, 231, 21-28.
25. Caporossi, G.; Hansen, P. Enumeration of polyhex hydrocarbons to h = 21. J. Chem. Inf. Comput. Sci. 1998, 38, 610-619.
26. Hansen, P.; Lebatteux, C.; Zheng, M. The boundary-edges code for polyhexes. J. Mol. Struct. (Theochem) 1996, 363, 237-247.
27. Herndon, W.; Bruce, A. J. Perimeter code for benzenoid aromatic hydrocarbons. Stud. Phys. Theor. Chem. 1987, 51, 491-513.
28. Avis, D.; Fukuda, K. Reverse search for enumeration. Discrete Appl. Mathematics 1996, 65, 21-46.
29. McKay, B. D. Isomorph-free exhaustive generation. J. Algorithms 1998, 26, 306-324.
30. Brunvoll, J.; Cyvin, S. J.; Cyvin, B. N.; Fuji, Z.; Guo, X. F. Theory of helicenic hydrocarbons 4. further enumeration. Struct. Chem. 1996, 7, 119-130.
31. Caporossi, G.; Hansen, P.; Zheng, M. Enumeration of fusenes to h = 20. In Discrete Mathematical Chemistry DIMACS Workshop March 23-25 1998; 2000; pp 63-78.
32. Guo, X.; Hansen, P.; Zheng, M. Boundary uniqueness of fusenes. Discrete Appl. Math. 2002, 118, 209-222.
33. Brinkmann, G.; Caporossi, G.; Hansen, P. A constructive enumeration of fusenes and benzenoids. J, Algorithms 2002, 45, 155-166.
34. McKay, B. D. Isomorph-free exhaustive generation. J. Algorithms 1998, 26, 306-324.
35. Grund, R.; Kerber, A.; Laue, R. MOLGEN - ein Computeralgebrasystem für die Konstruktion molekularer Graphen. Match 1992, 27, 87-131.
36. Brinkmann, G. Isomorphism rejection in structure generation programs. In Hansen, P., Fowler, P. W., Zheng, M., Eds.; Discrete Mathematical Chemistry, volume 51 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science; 2000, pp 25-38.
37. Aboav, D.; Gutman, I. Estimation of the number of benzenoid hydrocarbons. Chem. Phys. Lett. 1988, 148(1), 90-92.
38. Chyzak, F.; Gutman, I.; Paule, P. Predicting the number of hexagonal systems with 24 and 25 hexagons. Match 1999, 40, 139-151.
39. Brunvoll, J.; Cyvin, S. J.; Cyvin, B. N.; Fuji, Z.; Guo, X. F. Theory of helicenic hydrocarbons: 4. further enumeration. Struct. Chem. 1996, 7, 119-130.
40. Redelmeier, D. H. Counting polyominoes: Yet another attack Discrete Math 1981, 36, 191-203.