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arXiv · 2009.00699

On Generalised Petersen Graphs of Girth 7 that have Cop Number 4

Harmony Morris·Joy Morris
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Abstract

We show that if $n=7k/i$ with $i \in \{1,2,3\}$ 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 $7$.)

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Harmony Morris, Joy Morris. 2020-09-01. On Generalised Petersen Graphs of Girth 7 that have Cop Number 4. https://arxiv.org/abs/2009.00699

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