How to prove two graphs are isomorphic if and only if their complements are isomorphic? How this can be proved that two graphs $G_1$ and $G_2$ are isomorphic iff their complements are isomorphic? 

$G_1 \equiv G_2 \implies \exists$ a bijective function $f: V(G_1) \rightarrow V(G_2)$ such that $xy \in E(G_1) \iff f(x)f(y) \in E(G_2)$
Hints:


*

*Note since the vertex set of $G^c$ complement is the vertex set of $G$ itself. So $f$ can actually be considered a bijection from $V({G_1} ^ c ) \rightarrow V({G_2} ^ c )$

*How can the statement: $xy \in E(G_1) \iff f(x)f(y) \in E(G_2)$ be expressed in terms of a negative argument, (say $xy \not \in E(G_1)$)?? 

