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Which Graphs have only Self-Converse Orientations?

Published online by Cambridge University Press:  20 November 2018

Frank Harary ,
Edgar Palmer  and
Cedric Smith
Frank Harary
Affiliation:
University of Michigan and University College, London
Edgar Palmer
Affiliation:
University of Michigan and University College, London
Cedric Smith
Affiliation:
University of Michigan and University College, London
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An orientation of a graph G is an assignment of a unique direction to each line of G. The result is called an oriented graph. Two orientations of a graph are regarded as equivalent if the resulting oriented graphs are isomorphic as directed graphs. For example, the graph C3 consisting of a cycle of length 3 (a triangle) shown in Figure 1(a), has exactly two orientations D1 and D2; see Figure 1(b) and (c).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 425 - 429
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Harary, F., A seminar on graph theory. New York, Holt Rinehart and Winston, 1967, pp. 1-41.Google Scholar
2. Harary, F., Norman, R. and Cartwright, D., Structural models: an introduction to the theory of directed graphs. New York, Wiley, 1965.Google Scholar
3. Harary, F. and Palmer, E., On the number of orientations of a given graph. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 14(1966), pp. 125-128.Google Scholar
4. Harary, F. and Palmer, E., Enumeration of self-converse digraphs. Mathematika 13 (1966), pp. 151-157.Google Scholar
5. Kónig, D., Theorie der endlichen und unendlichen Graphen. Leipzig, 1936; reprinted New York, Chelsea, 1950.Google Scholar