A graph is an ordered pair (V,E). So, given a set V, graph will be different if E is different. Lets see how many different E we can get when |V| = 3.
For |V| = 3, we can have |E| = 0, 1, 2 or 3. So, 4 possible graphs.
Now, the question asks for |V| upto 3. So, we have to consider |V| = 2 and |V| = 1 also. When |V| = 2, we can have |E| = 1 or 0, so 2 possibilities. For |V| = 1, |E| can be only 0 and hence only one possibility. So, total number of possibilities is $$4 + 2 + 1 = 7$$.