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Graphical Regular Representations of Non-Abelian Groups, I

Published online by Cambridge University Press:  20 November 2018

Lewis A. Nowitz  and
Mark E. Watkins
Lewis A. Nowitz
Affiliation:
American Electric Power Service Corporation, 2 Broadway, New York, New York
Mark E. Watkins
Affiliation:
Syracuse University, Syracuse, New York
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In this paper, all groups and graphs considered are finite and all graphs are simple (in the sense of Tutte [8, p. 50]). If X is such a graph with vertex set V(X) and automorphism group A(X), we say that X is a graphical regular representation (GRR) of a given abstract group G if

(I) G ≅ A(X) , and

(II) A(X) acts on V(X) as a regular permutation group; that is, given u, v ∈ V(X), there exists a unique φ ∈ A(X) for which φ(u) = v.

That for any abstract group G there exists a graph X satisfying (I) is well-known (cf. [3]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 993 - 1008
Copyright
Copyright © Canadian Mathematical Society 1972

References

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