Is $G_2(V_2,E_2)$ a subgraph of $G_1(V_1,E_1)$ given number of vertices and adjacency matrix for both? Given $n_1$ and $n_2$ number of verteces and the adjacency matrix for both graphs, one should determine whether $G_2$ is a subgraph of $G_1$.

I am supposed to use C++ for this, and though I could probably come out with a solution including $20$ for functions, it's most likely not the best approach to the exercise.

Do I have to(?):


Assume the graphs have $n_2$ common vertices (because this has to be in order for $G_2$ to be a subgraph of $G_1$, right?)
Check to see if any of the $\begin{pmatrix}n_1\\ n_1-n_2\end{pmatrix}$ possibly resulting graphs after the removal of $n_1-n_2$ vertices from $G_1$ is equal to $G_2$


Althogh not sure how to compute the above.

This must be an easy exercise since it's for beginners in graphs, but I guess there's just something I am missing. Could you give me some hints on how to approach this in a better way? I've looked for this one a while, hopefully it's not a duplicate.
This problem is more general form of the graph isomorphism problem. No polynomial time algorithm is known solving it. The state of the art suggests possible approaches.