Destroying symmetry by orienting edges: Complete graphs and complete bigraphs

Frank Harary, Michael S. Jacobson
2001 Discussiones Mathematicae Graph Theory  
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
more » ... s ≤ 4 the values of t for which this number does exist.
doi:10.7151/dmgt.1139 fatcat:nwhyb7cypzfknjl7wqialpl3ju