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Discussiones Mathematicae Graph Theory 21(1) (2001) 149-158
DOI: https://doi.org/10.7151/dmgt.1139

DESTROYING SYMMETRY BY ORIENTING EDGES: COMPLETE GRAPHS AND COMPLETE BIGRAPHS

Frank Harary Department of Computer Science New Mexico State University Las Cruces, NM 88003, USA

Michael S. Jacobson Department of Mathematics University of Louisville Louisville, KY 40292, USA e-mail: mikej@louisville.edu

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 for s ≤ 4 the values of t for which this number does exist.

Keywords: oriented graph, automorphism group.

2000 Mathematics Subject Classification: 05C25.

References

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Received 21 December 1999
Revised 2 July 2001