Backtrack search and look-ahead for the construction of planar cubic graphs with restricted face sizes

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Volumn , Issue 48, 2003, Pages 163-177

  Brinkmann, Gunnar ^a   McKay, Brendan D ^b   Von Nathusius, Ulrike ^c  

^a BIELEFELD UNIVERSITY   (Germany)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c NONE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FULLERENE DERIVATIVE;

ALGORITHM; ARTICLE; CHEMICAL STRUCTURE; FILTER; MATHEMATICS; THEORETICAL STUDY;

EID: 0142169797     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. R.E.L. Aldred, S. Bau, D.A. Holton and B.D. McKay. Nonhamiltonian 3-connected cubic planar graphs. SIAM J. Discrete Math., 13:25-32, 2000.
2. D. Babic and N. Trinajstic. Resonance energies of fullerenes with 4-membered rings. Int. J. Quantum Chem., 55:309-314, 1995.
3. G. Brinkmann and M. Deza. Lists of face-regular polyhedra. Journal of Chemical Information and Computer Sciences, 40:530-541, 2000.
4. G. Brinkmann and A.W.M. Dress. A constructive enumeration of fullerenes. Journal of Algorithms, 23:345-358, 1997.
5. G. Brinkmann, O. Heidemeier, and T. Harmuth. The construction of cubic and quartic planar maps with prescribed face degrees. to appear in Discrete Applied Mathematics.
6. G. Brinkmann and B.D. McKay. Fast generation of non-isomorphic planar cubic graphs. in preparation, see http://cs.anu.edu.au/~bdm/index.html.
7. O. Delgado Friedrichs, A.W.M. Dress, A. Müller, and M.T. Pope. Polyoxometalates: A class of compounds with remarkable topology. Molecular Engineering, 3:9-28, 1993.
8. V. Eberhard. Zur Morphologie der Polyeder. Teubner, 1891.
9. B. Grünbaum. Convex Polytopes. John Wiley & Sons, Ltd., London, New York, Sydney, 1967.
10. 60: Buckminsterfullerene. Nature, 318:162-163, 1985.
11. J. Malkevitch. Polytopal graphs. In L.W. Beineke and R.J. Wilson, editors, Selected Topics in Graph Theory, volume 3, pages 169-188. 1988.
12. 70. Chemical Physics letters, 181(2,3):105-111, 1991.
13. B.D. McKay. Isomorph-free exhaustive generation. Journal of Algorithms, 26:306-324, 1998.
14. E. Steinitz and H. Rademacher. Vorlesungen über die Theorie der Polyeder. Springer, Berlin, 1934.