Destroying symmetry by orienting edges: Complete graphs and complete bigraphs

  title={Destroying symmetry by orienting edges: Complete graphs and complete bigraphs},
  author={Frank Harary and Michael S. Jacobson},
  journal={Discussiones Mathematicae Graph Theory},
Our purpose is to introduce the concept of determining the smallest number of edges of a graph which can be oriented so that the resulting mixed graph has the trivial automorphism group. We find that this number for complete graphs is related to the number of identity oriented trees. For complete bipartite graphs Ks,t, s ≤ t, this number does not always exist. We determine for s ≤ 4 the values of t for which this number does exist. 

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