Name
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 $7$.) |
Year | DOI | Venue |
|---|---|---|
2022 | 10.26493/2590-9770.1382.2ad | The Art of Discrete and Applied Mathematics |
DocType | Volume | Issue |
Journal | 5 | 2 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Harmony Morris | 1 | 0 | 0.34 |
| Joy Morris | 2 | 78 | 16.06 |