Isoperimetric quotient for fullerenes and other polyhedral cages

Journal of Chemical Information and Computer Sciences

Volumn 37, Issue 6, 1997, Pages 1028-1032

  Pisanski, Tomaž ^a   Kaufman, Matjaž ^a   Bokal, Drago ^a   Kirby, Edward C ^b   Graovac, Ante ^c  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b Resource Use Institute   (United Kingdom)

^c RUDER BO KOVI INSTITUTE   (Croatia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CALCULATIONS; CHEMICAL ANALYSIS; DRAWING (GRAPHICS); GEOMETRY; GRAPHIC METHODS; LAPLACE TRANSFORMS; MOLECULAR DYNAMICS; STRAIN;

ISOPERIMETRIC QUOTIENT; POLYHEDRAL CAGES;

FULLERENES;

EID: 0031276667     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci970228e     Document Type: Article

References (27)

1. 60: Buckminsterfullerene. Chem. Rev. 1991, 91, 1213-1235.
2. Thurston, W. P. Res. report GCG 7: Geometry Center: University of Minnesota, 1991.
3. Brinkmann, G.; Dress,A. W. M. A Constructive Enumeration of Fullerenes. J. Algorithms To appear.
4. n, with n = 24, 28, 32, 36, 50, 60, 70, Nature 1987, 329, 529-531.
5. Schmalz, T. G.; Seitz, W. A.; Klein, D. J.; Hite, G. E. Elemental Carbon Cages. J. Am. Chem. Soc. 1988, 110, 1113-1127.
6. Plestenjak, B.; Pisanski, T.; Graovac, A. Generating Fullerenes at Random. J. Chem. Inf. Comput. Sci. 1996, 36, 825-828.
7. Klein, D. J.; Liu, X. Elemental Carbon Isomerism. Internat. J. Quant. Chem.: Quantum Chem. Symp. 1994, 28, 501-523.
8. Klein, D. J.; Zhu, Z. All-Conjugated Carbon Species. In From Chemical Topology to Three-Dimensional Geometry; Balaban, Ed.; Plenum Press: New York, 1997; pp 297-341.
9. Polya, G. Induction and analogy in mathematics: Princeton University Press: pp Princeton, 1954.
10. Deza, A.; Deza, M.; Grishukhin, W. Embeddings into Half-Cubes of Fullerenes, Virus Capisides, Geodesic Domes and Coordinations Polyhedra. Submitted for publication.
11. Fruchterman, T.; Reingold, E. Graph Drawing by Force-Directed Placement. Software-Practice and Experience 1991, 21, 1129-1164.
12. Pisanski, T.; Plestenjak, B.; Graovac, A. NiceGraph Program and its Applications In Chemistry. Croat. Chem. Acta 1995, 68, 283-292.
13. Vega Version 0.2 Quick Reference Manual and Vega Graph Gallery; Pisanski, T., Ed.; DMFA: Jadranska 19, SI-1000 Ljubljana, Slovenia, 1995.
14. Pisanski, T., et al. Vega: System for manipulating discrete mathematical structures. Available at http://vega.ijp.si/.
15. Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A. Graph-drawing algorithms geometries versus molecular mechanics in fullerenes. Chem. Phys. Lett. 1996; 259, 420-424.
16. Eades, P. A Heuristic for Graph Drawing. Congressus Numerantium 1984, 42, 149-160.
17. Davidson, R.; Harel, D. Drawing Graphs Nicely Using Simulated Annealing. ACM Transactions on Graphics 1996, 15, 301-331.
18. Harel, D.; Sardas, M. Randomized Graph Drawing with Heavy-Duty Preprocessing. J. Visual Lang. Comput. 1995, 6, 233-253.
19. Harel, D.; Sardas, M. An Algorithm for Straight-Line Drawing of Planar Graphs. Algorithmica To appear.
20. Fowler, P. W.; Pisanski, T.; Shawe-Taylor, J. Molecular Graph Eigenvectors for Molecular Coordinates. In Graph Drawing, Lecture Notes in Computer Science; Tamassia, R., Tollis, I. G., Eds.; Springer Verlag: Berlin, 1995, Vol. 894, pp 282-285.
21. Shawe-Taylor, J.; Pisanski, T. Characterizing graph drawing with eigenvectors; Technical Report CSD-TR-93-20, Royal Holloway, University of London Department of Computer Science, Egham, Surrey TW20 OEX, England, 1993.
22. Manolopoulos, D. E.; Fowler, P. W. Molecular Graphs, Point Groups and Fullerenes. J. Chem. Phys. 1992, 96, 7603-7614.
23. Ringel, G. Map Color Theorem; Springer-Verlag: Berlin and New York, 1974.
24. Fowler, P.; Pisanski, T. Leapfrog Transformations and Polyhedra of Clar Type. J. Chem. Soc. Faraday Trans. 1994, 90(19), 2865-2871.
25. Jiang, Y.; Shao, Y.; Kirby, E. Topology and Stability of Trivalent Polyhedral Clusters. Fullerene Science Technol. 1994, 2, 481-497.
26. Fowler, P. W.; Manolopoulos, D. E. An Atlas of Fullerenes; Clarendon Press: 1995.
27. 100 are available on http://cochem2.tutkie.tut.ac.-jp:8000/member/yoshida/higher/higherE.html.