ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory


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


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

Dedicated to the memory of ``Uncle'' Paul Erdős who stimulated
and the research careers of many mathematicians.


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.


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Received 21 December 1999
Revised 2 July 2001