Automorphism of Graph $G^n$ I try to define the automorphism of $G^n$ where $G$ is a graph and $G^n = G \Box \ldots \Box G$,( $n$ times, $\Box$  is the graph product).
I think that : $\text{Aut}(G^n)$ is $\text{Aut}(G) \wr  S_n$ where $S_n$ is the symmetric group of $\{1,\ldots,n\}$ but I have no idea how to prove it because I am a beginner in group theory. Can you help me or suggest me a reference on this subject ?  Thanks a lot.

You are right, provided you assume that $G$ is prime relative to the Cartesian product, the automorphism group of the $n$-th Cartesian power of $G$ is the wreath product as you stated.
The standard reference for this is Hammack, Richard; Imrich, Wilfried; Klavžar, Sandi: Handbook of product graphs. (There is an older version of this, written by Imrich and Klavžar alone, which would serve just as well.) Unfortunately there does not seem to be much on the internet on this subject.
