Symmetry Breaking in Graphs

@article{Albertson1996SymmetryBI,
  title={Symmetry Breaking in Graphs},
  author={Michael O. Albertson and Karen L. Collins},
  journal={Electr. J. Comb.},
  year={1996},
  volume={3}
}
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
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