Finding lower bound for $\alpha(G) + \omega(G)$

Question

I'm wondering to find a lower bound for $\alpha(G) + \omega(G)$. In my tries, I couldn't find a graph without inequation: $\alpha(g).\omega(G) \geq |V(G)|$ Thus I think one possible bound is $\alpha(G) + \omega(G) \geq 2\sqrt n$, but I have no proof for this bound.