Distinguishing colorings of Cartesian products of complete graphs

  title={Distinguishing colorings of Cartesian products of complete graphs},
  author={Michael J. Fisher and Garth Isaak},
  journal={Discrete Mathematics},
We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph Ks,t which admits only the identity automorphism. In particular this allows us to determine the distinguishing number of the Cartesian product of complete graphs. The distinguishing number of a graph is the minimum number of colors needed to label the vertices so that the only color preserving automorphism is the identity. The distinguishing number was introduced by Albertson and… CONTINUE READING
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