  We consider the minimum order graphs with a given cop number. We prove that
the minimum order of a connected graph with cop number 3 is 10, and show that
the Petersen graph is the unique isomorphism type of graph with this property.
We provide the results of a computational search on the cop number of all
graphs up to and including order 10. A relationship is presented between the
minimum order of graph with cop number $k$ and Meyniel's conjecture on the
asymptotic maximum value of the cop number of a connected graph.
