On generalised Petersen graphs of girth 7 that have cop number 4
| dc.contributor.author | Morris, Harmony | |
| dc.contributor.author | Morris, Joy | |
| dc.date.accessioned | 2025-12-11T18:16:22Z | |
| dc.date.available | 2025-12-11T18:16:22Z | |
| 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 show that if n = 7k/i with i ∈ {1, 2, 3} then the cop number of the generalised Petersen graph GP(n,k) is 4, with some small previously-known exceptions. It was previously proved by Ball et al. (2015) that the cop number of any generalised Petersen graph is at most 4. The results in this paper explain all of the known generalised Petersen graphs that actually have cop number 4 but were not previously explained by Morris et al. in a recent preprint, and places them in the context of infinite families. (More precisely, the preprint by Morris et al. explains all known generalised Petersen graphs with cop number 4 and girth 8, while this paper explains those that have girth 7.) | |
| dc.description.peer-review | Yes | |
| dc.identifier.citation | Morris, H., & Morris, J. (2022). On generalised Petersen graphs of girth 7 that have cop number 4. The Art of Discrete and Applied Mathematics, 5(2), Article #P2.05. https://doi.org/10.26493/2590-9770.1382.2ad | |
| dc.identifier.uri | https://hdl.handle.net/10133/7253 | |
| 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/10.26493/2590-9770.1382.2ad | |
| dc.subject | Cops and robbers | |
| dc.subject | Generalised Petersen graphs | |
| dc.subject | Girth | |
| dc.subject | Cop number | |
| dc.title | On generalised Petersen graphs of girth 7 that have cop number 4 | |
| dc.type | Article |