How to prove graph isomorphism is NP?
You haven't explained what graph isomorphism means for you, so let me assume that you mean the language of all pairs of graphs $(G_1,G_2)$ which are isomorphic.

Two graphs $G_1 = (V_1,E_1),G_2 = (V_2,E_2)$ are isomorphic if there exists a bijection $f\colon V_1 \to V_2$ such that $(x,y) \in E_1$ iff $(f(x),f(y)) \in E_2$.

You take it from here.