Let $G$ be a disconnected graph. Then, I know $\bar G$ is connected. Prove that if $u$ and $v$ are any two vertices of $\bar G$, then $d\_{\bar G}(u,v)=1$ or $d\_{\bar G}(u,v)=2$

Then I also know if $G$ is disconnected, $diam(\bar G) \leq 2$.