The distinguishing number of the augmented cube and hypercube powers

Discrete Mathematics

Volumn 308, Issue 11, 2008, Pages 2330-2336

  Chan, Melody ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Augmented cube; Distinguishing number; Hypercube; Symmetry breaking

Indexed keywords

COMPUTATION THEORY; FINITE DIFFERENCE METHOD; GRAPH THEORY; NUMERICAL METHODS;

AUGMENTED CUBE; DISTINGUISHING NUMBER; SYMMETRY BREAKING;

NUMBER THEORY;

EID: 40649102710     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2006.09.056     Document Type: Article

References (21)

1. Albertson M., and Collins K. An introduction to symmetry breaking in graphs. Graph Theory Notes N.Y. 30 (1996) 6-7
2. Albertson M., and Collins K. Symmetry breaking in graphs. Electron. J. Combin. 3 (1996)
3. Bogstad B., and Cowen L. The distinguishing number of the hypercube. Discrete Math. 283 (2004) 29-35
4. Chan M. The distinguishing number of the direct product and wreath product action. J. Algebraic Combin. 24 3 (2006)
5. Chan M. The maximum distinguishing number of a group. Electron. J. Combin. 13 (2006)
6. C.T. Cheng, Three problems in graph labeling, Ph.D. Thesis, Department of Mathematical Sciences, Johns Hopkins University, 1999.
7. Cheng C.T. On computing the distinguishing numbers of trees and forests. Electron. J. Combin. 13 (2006)
8. J. Choi, S. Hartke, H. Kaul, Distinguishing chromatic number of Cartesian products of graphs, preprint, 2005.
9. S.A. Choudum, V. Sunitha, Automorphisms of augmented cubes, Technical report, Department of Mathematics, Indian Institute of Technology Madras, Chennai, March 2001.
10. Choudum S.A., and Sunitha V. Augmented cubes. Networks 40 (2002) 71-84
11. Collins K., and Trenk A. The distinguishing chromatic number. Electron. J. Combin. 13 (2006)
12. Imrich W., and Klavzar S. Distinguishing Cartesian powers of graphs. J. Graph Theory 53 (2006)
13. Klavzar S., Wong T., and Zhu X. Distinguishing labelings of group action on vector spaces and graphs. J. Algebra 303 (2006)
14. Klavzar S., and Zhu X. Cartesian powers of graphs can be distinguished with two labels. European J. Combin. 28 (2007)
15. Miller Z., and Perkel M. Aust. J. Combin. 10 (1994) 17-28
16. Open problems column, SIAM Activity Group Newsletter in Discrete Mathematics, Summer-Fall 1996, No. 23, archived at 〈http://www.math.uiuc.edu/∼west/pcol/pcolink.html〉.
17. K. Potanka, Groups, graphs and symmetry breaking, Masters Thesis, Department of Mathematics, Virginia Polytechnic Institute, 1998.
18. Russell A., and Sundaram R. A note on the asymptotics and computational complexity of graph distinguishability. Electron. J. Combin. 5 (1998)
19. Tymoczko J. Distinguishing numbers for graphs and groups. Electron. J. Combin. 11 1 (2004)
20. T. Wong, X. Zhu, Distinguishing labeling of group actions, preprint, 2005.
21. T. Wong, X. Zhu, Distinguishing sets of the actions of symmetric groups, preprint, 2005.