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.