# Cops and robbers on directed and undirected abelian Cayley graphs

@article{Bradshaw2021CopsAR, title={Cops and robbers on directed and undirected abelian Cayley graphs}, author={Peter Bradshaw and Seyyed Aliasghar Hosseini and J'er'emie Turcotte}, journal={Eur. J. Comb.}, year={2021}, volume={97}, pages={103383} }

We discuss the game of cops and robbers on abelian Cayley graphs. We improve the upper bound for cop number in the undirected case, and we give an upper bound for the directed version. We also construct Meyniel extremal families of graphs with cop number $\Theta (\sqrt{n})$.

## One Citation

On the cop number of graphs of high girth

- Mathematics, Computer ScienceArXiv
- 2020

It is shown that the "weak" Meyniel's conjecture holds for expander graph families of bounded degree and that the cop number of any graph with girth $g$ and minimum degree $\delta$ is at least $\tfrac{1}{g}(\delta - 1)^{\lfloor g-1}{4}\rfloor}$.

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