  In this short paper we study the game of Cops and Robbers, played on the
vertices of some fixed graph $G$ of order $n$. The minimum number of cops
required to capture a robber is called the cop number of $G$. We show that the
cop number of graphs of diameter 2 is at most $\sqrt{2n}$, improving a recent
result of Lu and Peng by a constant factor. We conjecture that this bound is
still not optimal, and obtain some partial results towards the optimal bound.
