# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

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# Discussiones Mathematicae Graph Theory

## 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 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.

Keywords: oriented graph, automorphism group.

2000 Mathematics Subject Classification: 05C25.

## References

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