Graphical Regular Representations of Non-Abelian Groups, I

Lewis A. Nowitz, Mark E. Watkins

Type: Article

Publication Date: 1972-12-01

Citations: 86

DOI: https://doi.org/10.4153/cjm-1972-101-5

Abstract

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 ]).

Locations

Canadian Journal of Mathematics - View - PDF

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Works Cited by This (3)

Action	Title	Year	Authors
+	Connectivity in Graphs	1966	W. T. Tutte
+	Generators and Relations for Discrete Groups	1972	H. S. M. Coxeter W. O. J. Moser
+	Generators and Relations for Discrete Groups	1957	H. S. M. Coxeter W. O. J. Moser