Detecting graphical and digraphical regular representations in groups of squarefree order

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Date
2025
Authors
Morris, Joy
Verret, Gabriel
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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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Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Squarefree order , Caley , DRR-detecting , GRR-detecting , Graphical , Digraphical
Citation
Morris, J., & Verret, G. (2025). Detecting graphical and digraphical regular representations in groups of squarefree order. Electronic Journal of Combinatorics, 32(2). Article P2.38. https://doi.org/10.37236/12476
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https://hdl.handle.net/10133/7215
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Morris, Joy