Most rigid representations and Cayley index
| dc.contributor.author | Morris, Joy | |
| dc.contributor.author | Tymburski, Josh | |
| dc.date.accessioned | 2025-12-13T21:42:27Z | |
| dc.date.available | 2025-12-13T21:42:27Z | |
| dc.date.issued | 2018 | |
| dc.description | Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies | |
| dc.description.abstract | For any finite group G, a natural question to ask is the order of the smallest possible automorphism group for a Cayley graph on G. A particular Cayley graph whose automorphism group has this order is referred to as an MRR (Most Rigid Representation), and its Cayley index is a numerical indicator of this value. Study of GRRs showed that with the exception of two infinite families and thirteen individual groups, every group admits a Cayley graph whose MRR is a GRR, so that the Cayley index is 1. The full answer to the question of finding the smallest possible Cayley index for a Cayley graph on a fixed group was almost completed in previous work, but the precise answers for some finite groups and one infinite family of groups were left open. We fill in the remaining gaps to completely answer this question. | |
| dc.description.peer-review | Yes | |
| dc.identifier.citation | Morris, J. & Tymburki, J. (2018). Most rigid representations and Cayley index. The Art of Discrete and Applied Mathematics, 1, Article #P1.05. https://doi.org/10.26493/2590-9770.1242.809 | |
| dc.identifier.uri | https://hdl.handle.net/10133/7260 | |
| 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.url | https://doi.org/10.26493/2590-9770.1242.809 | |
| dc.subject | Cayley graph | |
| dc.subject | Cayley index | |
| dc.subject | GRR | |
| dc.subject | MRR | |
| dc.subject | Automorphisms | |
| dc.title | Most rigid representations and Cayley index | |
| dc.type | Article |