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Destroying symmetry by orienting edges: Complete graphs and complete bigraphs
2001
Discussiones Mathematicae Graph Theory
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Dedicated to the memory of "Uncle" Paul Erdős who stimulated and the research careers of many mathematicians. Abstract 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
doi:10.7151/dmgt.1139
fatcat:nwhyb7cypzfknjl7wqialpl3ju