Geodesic
Destroying symmetry by orienting edges: complete graphs and complete bigraphs
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 149-158

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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 K_s,t, s ≤ t, this number does not always exist. We determine for s ≤ 4 the values of t for which this number does exist.
Keywords: oriented graph, automorphism group 
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Harary, Frank; Jacobson, Michael. Destroying symmetry by orienting edges: complete graphs and complete bigraphs. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 149-158. http://geodesic.mathdoc.fr/item/DMGT_2001_21_2_a0/