Symmetry Breaking in Graphs

  title={Symmetry Breaking in Graphs},
  author={Michael O. Albertson and Karen L. Collins},
  journal={Electr. J. Comb.},
A labeling of the vertices of a graph G, : V (G) ! f1; : : : ; rg, is said to be r-distinguishing provided no automorphism of the graph preserves all of the vertex labels. The distinguishing number of a graph G, denoted by D(G), is the minimum r such that G has an r-distinguishing labeling. The distinguishing number of the complete graph on t vertices is t. In contrast, we prove (i) given any group , there is a graph G such that Aut(G) = and D(G) = 2; (ii) D(G) = O(log(jAut(G)j)); (iii) if Aut… CONTINUE READING
Highly Influential
This paper has highly influenced 17 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
96 Citations
13 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 13 references

Which Way Did the Bicycle Go

  • J. Konhauser, D. Velleman, S. Wagon
  • Dolciani series, Mathematical Association of…
  • 1996
1 Excerpt

An Introduction to the Theory of Groups

  • Joseph J. Rotman
  • 1995

The Petersen Graph

  • D. A. Holton, J. Sheehan
  • Cambridge Univer- sity Press, New York
  • 1993
1 Excerpt


  • J. Kobler
  • Schoning, and J.Toran, The Graph Isomorphism…
  • 1993
1 Excerpt

Graphs, Groups and Surfaces

  • Arthur T. White
  • North Holland Math Studies
  • 1984

mann, Group Theoretic Algorithms and Graph Isomor- phism

  • Christoph Ho
  • Science
  • 1982
1 Excerpt

Problem 729 in Journal of Recreational Mathematics, vol- ume 11, (solution in volume

  • Frank Rubin
  • 1980
1 Excerpt

Graph Theory, Springer-Verlag, New York, 1979, Grad- uate Texts in Mathematics

  • Bela Bollobas
  • 1979

Permutation Groups and Combinatorial Structures

  • N. L. Biggs, A. T. White
  • Cambridge Univ. Press, New York
  • 1979

Regular Polytopes

  • H.S.M. Coxeter
  • Dover, New York
  • 1973
1 Excerpt

Similar Papers

Loading similar papers…