Chirality of toroidal molecular graphs

Journal of Chemical Information and Modeling

Volumn 45, Issue 6, 2005, Pages 1527-1535

  Kutnar, Klavdija ^a   Malnič, Aleksander ^b   Marušič, Dragan ^a,b  

^a UNIVERSITY OF PRIMORSKA   (Slovenia)

^b INSTITUTE OF MATHEMATICS   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MOLECULAR DYNAMICS;

CAYLEY GRAPHS; MOLECULAR GRAPHS; VERTICES;

MOLECULAR GRAPHICS;

EID: 28944438264     PISSN: 15499596     EISSN: 1549960X     Source Type: Journal    
DOI: 10.1021/ci050211t     Document Type: Conference Paper

References (33)

1. Deza, M.; Fowler, P. W.; Rossat, A.; Rogers, K. M. Fullerenes as tilings of surfaces. J. Chem. Inf. Comput. Sci. 2000, 9, 550-558.
2. Diudea, M. V.; Kirby, E. C. The energetic stability of tori and single-wall tubes. Fullerene Sci. Technol. 2001, 9, 445-465.
3. Diudea, M. V.; Silaghi-Dumitrescu, I.; Parv, B. Toranes versus torenes, MATCH 2001, 44, 117-133.
4. Diudea, M. V. Topology of naphthylenic tori. Phys. Chem. Chem. Phys. 2002, 19, 4740-4746.
5. Diudea, M. V. Toroidal graphenes from 4-valent tori. Bull. Chem. Soc. Jpn. 2002, 75, 487-492.
6. Diudea, M. V.; John, P. E.; Graovac, A.; Primorac, M.; Pisanski, T. Leapfrog and related operations on toroidal fullerenes. Croat. Chem. Acta 2003, 76, 153-159.
7. Diudea, M. V.; Parv, B.; Kirby, E. C. Azulenic tori. MATCH 2003, 47, 53-70.
8. Diudea, M. V.; Janežič, D.; Graovac, A. Topology counting in nanostructures. Carpath. J. Math. 2004, 20, 223-234.
9. Kirby, E. C.; Mallion, R. B.; Pollak, P. Toroidal polyhexes. J. Chem. Soc., Faraday Trans. 1993, 89, 1945-1953.
10. Graovac, A.; Plavšič, D.; Kaufman, M.; Kirby, E. C.; Pisanski, T. Application of the adjacency matrix eigenvectors method to geometry determination of toroidal carbon molecules. J. Chem. Phys. 2000, 113, 1925-1931.
11. John, P. E.; Kekulé count in toroidal hexagonal carbon cages. Croat. Chem. Acta 1998, 71, 435-447.
12. Kirby, E. C.; Pollak, P. How to enumerate the connectional isomers of a toroidal polyhex fullerene. J. Chem. Inf. Comput. Sci. 1998, 38, 66-70.
13. Lijnen, E.; Ceulemans, A. Oriented 2-cell embeddings of a graph and their symmetry classification: generating algorithms and case study of the Moebius-Kantor graph. J. Chem. Inf. Comput. Sci. 2004, 44, 1552-1564.
14. Xiao, J. Y.; Hosoya, H. Analysis of the relationship among the graphs isomorphic to multilayered cyclic fence graphs (MLCFG). J. Chem. Inf. Comput. Sci. 2002, 42, 1004-1010.
15. Liu, J.; Dai, H. J.; Hafner, J. H.; Colbert, D. T.; Smalley, D. T. R. E.; Tans, S. T.; Dekker, C. Fullerene crop circles. Nature 1997, 385, 780-781.
16. Altshuler, A. Hamiltonian circuits in some maps on the torus. Discrete Math. 1972, 1, 299-314.
17. Altshuler, A. Construction and enumeration of regular maps on the torus. Discrete Math. 1973, 4, 201-217.
18. Thomassen, C. Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface. Trans. Am. Math. Soc. 1991, 323, 605-635.
19. The Foster Census; Bouwer, I. Z., Ed.; Charles Babbage Research Centre: Winnipeg, Canada, 1988.
20. Conder, M. D. E.; Dobcsanyi, P. Trivalent symmetric graphs on up to 768 vertices. J. Comb. Math. Comb. Comput. 2002, 40, 41-63.
21. Marušič, D.; Pisanski, T. Symmetries of hexagonal molecular graphs on the torus. Croat. Chem. Acta 2000, 73, 969-981.
22. Tutte, W. T. A family of cubical graphs. Proc. Cambridge Philos. Soc. 1947, 43, 459-474.
23. Bosma, W.; Cannon, J.; Playoust, C. The MAGMA Algebra System I: The User Language. J. Symbolic Comput. 1997, 24, 235-265.
24. Biggs, N. L.; White, A. T. Permutation groups and combinatorial structures; Cambridge University Press: New York, 1979.
25. Bondy, A.; Murty, U. S. R. Graph Theory with Applications; American Elsevier Co.: New York, 1976.
26. Coxeter, H. S. M.; Moser, W. O. J. Generators and Relators for Discrete Groups, 4th ed.; Springer-Verlag: New York, 1980.
27. Wielandt, H. Finite Permutation Groups; Academic Press: New York, 1964.
28. Hladnik, M.; Marušič, D.; Pisanski, T. Cyclic Haar graphs. Discrete Math. 2002, 244, 137-152.
29. Gross, J. L.; Tucker, T. W. Topological Graph Theory; Wiley Interscience: New York, 1987.
30. Malnič, A.; Nedela, R.; Škoviera, M. Lifting graph automorphisms by voltage assignments. Eur. J. Combin. 2000, 21, 927-947.
31. Malnič, A.; Marušič, D.; Potočnik, P. Elementary abelian covers of graphs. J. Algebr. Comb. 2004, 20, 71-97.
32. 2. Eur. J. Combin. 2005, in print.
33. Biggs, N. L. Aspects of symmetry in graphs, Algebraic methods in graph theory. Colloq. Math. Soc. Janos Bolyai; North-Holland: Amsterdam-New York, 1981; Vols. I and II (Szeged, 1978), pp 27-35.