While this is reasonable question, I have never seen it.

I think that we must assume that these are labeled graphs.

On n labeled vertices there are

possible graphs.

Now each of those is a subgraph of

.

However, that is not the answer to this question because each of those includes all of the vertices.

AND that does not need to be the case. As of now, I do know how to expand that number.

Any of these graphs that have vertices of degree zero can be multiple subgraphs.

Thus, how do we count all of those possibilities?

I hope this helps.