On generalised Petersen graphs of girth 7 that have cop number 4
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Date
2022
Authors
Morris, Harmony
Morris, Joy
Journal Title
Journal ISSN
Volume Title
Publisher
University of Primorska
The Slovenian Discrete and Applied Mathematics Society
The Slovenian Discrete and Applied Mathematics Society
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.)
Description
Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Cops and robbers , Generalised Petersen graphs , Girth , Cop number
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