Detecting Graphical and Digraphical Regular Representations in groups of squarefree order
Abstract
A necessary condition for a Cayley digraph Cay(R,S) to be a regular representation is that there are no non-trivial group automorphisms of R that fix S setwise. A group is DRR-detecting or GRR-detecting if this condition is also sufficient for all Cayley digraphs or graphs on the group, respectively. In this paper, we determine precisely which groups of squarefree order are DRR-detecting, and which are GRR-detecting.
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