Geodesic
Detecting graphical and digraphical regular representations in groups of squarefree order
Joy Morris ; Gabriel Verret1
1University of Auckland
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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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.
DOI : 10.37236/12476
Classification : 05C25, 05C20
Mots-clés : Cayley digraph, DRR detecting groups, GRR-detecting groups

Joy Morris    ; Gabriel Verret  1

1 University of Auckland 
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     author = {Joy Morris and Gabriel Verret},
     title = {Detecting graphical and digraphical regular representations in groups of squarefree order},
     journal = {The electronic journal of combinatorics},
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Joy Morris; Gabriel Verret. Detecting graphical and digraphical regular representations in groups of squarefree order. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/12476

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