Groups for which it is easy to detect graphical regular representations
| dc.contributor.author | Morris, Dave W. | |
| dc.contributor.author | Morris, Joy | |
| dc.contributor.author | Verret, Gabriel | |
| dc.date.accessioned | 2025-12-12T19:42:38Z | |
| dc.date.available | 2025-12-12T19:42:38Z | |
| dc.date.issued | 2022 | |
| dc.description | Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies | |
| dc.description.abstract | We say that a finite group G is DRR-detecting if, for every subset S of G, either the Cayley digraph Cay(G,S) is a digraphical regular representation (that is, its automorphism group acts regularly on its vertex set) or there is a nontrivial group automorphism φ of G such that φ(S) = S. We show that every nilpotent DRR-detecting group is a p-group, but that the wreath product Zp wr Zp is not DRR-detecting, for every odd prime p. We also show that if G1 and G2 are nontrivial groups that admit a digraphical regular representation and either gcd(|G1|, |G2|) = 1, or G2 is not DRR-detecting, then the direct product G1 x G2 is not DRR-detecting. Some of these results also have analogues for graphical regular representations. | |
| dc.identifier.citation | Morris, D. W., Morris, J., & Verret, G. (2022). Groups for which it is easy to detect graphical regular representations. The Art of Discrete and Applied Mathematics, 5(1), Article #P1.07. https://doi.org/10.26493/2590-9770.1373.60a | |
| dc.identifier.uri | https://hdl.handle.net/10133/7254 | |
| dc.language.iso | en | |
| dc.publisher | University of Primorska | |
| dc.publisher | The Slovenian Discrete and Applied Mathematics Society | |
| dc.publisher.department | Department of Mathematics and Computer Science | |
| dc.publisher.faculty | Arts and Science | |
| dc.publisher.institution | University of Lethbridge | |
| dc.publisher.institution | University of Auckland | |
| dc.subject | Cayley graph | |
| dc.subject | GRR | |
| dc.subject | DRR | |
| dc.subject | Automorphism group | |
| dc.subject | Normalizar | |
| dc.title | Groups for which it is easy to detect graphical regular representations | |
| dc.type | Article |