Graphical Regular Representations of Non-Abelian Groups, I
- 1 December 1972
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 24 (6) , 993-1008
- 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]). IfXis such a graph with vertex setV(X)and automorphism groupA(X),we say thatXis agraphical regular representation(GRR) of a given abstract groupGif(I) G ≅ A(X) , and(II)A(X)acts onV(X) as a regular permutation group; that is, givenu, v∈V(X), there exists a uniqueφ∈A(X)for whichφ(u) =v.That for any abstract groupGthere exists a graphXsatisfying (I) is well-known (cf. [3]).Keywords
This publication has 2 references indexed in Scilit:
- Connectivity in GraphsPublished by University of Toronto Press Inc. (UTPress) ,1966
- Generators and Relations for Discrete GroupsPublished by Springer Nature ,1957