The distinguishing number of the direct product and wreath product action

Journal of Algebraic Combinatorics

Volumn 24, Issue 3, 2006, Pages 331-345

  Chan, Melody ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Direct product; Distinguishing number; Symmetry breaking; Symmetry group; Wreath product

Indexed keywords

COMBINATORIAL MATHEMATICS; GRAPH THEORY; MATHEMATICAL OPERATORS; NUMERICAL METHODS; SET THEORY;

CARTESIAN PRODUCT; DIRECT PRODUCT; DISTINGUISHING NUMBER; SYMMETRY BREAKING; SYMMETRY GROUP; WREATH PRODUCT;

LINEAR ALGEBRA;

EID: 33747893135     PISSN: 09259899     EISSN: 15729192     Source Type: Journal    
DOI: 10.1007/s10801-006-0006-7     Document Type: Article

References (13)

1. M. Albertson and K. Collins, "An introduction to symmetry breaking in graphs," Graph Theory Notes N.Y. 30 (1996), 6-7.
2. M. Albertson and K. Collins, "Symmetry breaking in graphs," Electronic J. Combin. 3 (1996).
3. B. Bogstad and L. Cowen, "The distinguishing number of the hypercube," Discrete Math. 283 (2004), 29-35.
4. P.J. Cameron, Permutation Groups, in Handbook of Combinatorics, R.L. Graham, M. Grötschel, L. Lovász (eds.), Cambridge, 1995, vol. 1, pp. 611-645.
5. M. Chan, "The distinguishing number of the augmented cube and hypercube powers," preprint, available at http://aixiv.org/pdf/math.CO/ 0601361
6. M. Chan, "The maximum distinguishing number of a group," to appear in Electronic J. Combinatorics, available at http://arxiv.org/pdf/math. CO/0601359.
7. C.C.T. Cheng, "Three problems in graph labeling," Ph.D. Thesis, Department of Mathematical Sciences, Johns Hopkins University, 1999.
8. E. Dobson and J. Morris, "Automorphism groups of wreath product digraphs," submitted.
9. M. Hall, The Theory of Groups, Macmillan, New York, 1959.
10. R.L. Hemminger, "The lexicographic product of graphs," Duke Math. J. 33 (1966), 499-501.
11. K. Potanka, "Groups, graphs and symmetry breaking," Masters Thesis, Department of Mathematics, Virginia Polytechnic Institute, 1998.
12. G. Sabidussi, "The composition of graphs," Duke Math. J. 26 (1959), 693-696.
13. J. Tymoczko, "Distinguishing numbers for graphs and groups," Electronic J. Combin. 11(1) (2004).