In the question that came in GATE 1994 , it is just asking number of simple graphs having upto 3 vertices and hence we should not bother about connectivity..
And in the question which came in GATE 2001 , it asked about the number of simple graphs of n vertices which is not necessarily connected which means it may be connected or may not be.So we have to include both types of graphs and hence connectivity is not a concern here as well..
So for both of them , the answer would be : 2^{(n(n-1)/2)} as we can have maximum of n(n-1) / 2 edges and each edge can be selected or rejected for formation of the graph..
However if we are asked : Number of simple undirected graphs which are necessarily connected and has 'n' vertices , then this problem's complexity becomes higher as we need to take connectivity for each graph into consideration as well..
For labelled graphs of n vertices , the following recurrence is used :
Σ ^{n}C_{k }* k * d_{k }* 2^{(n-k)(n-k-1)/2} = n * 2^{n(n-1)/2} where d_{n} is the number of labelled, connected, simple graphs on n vertices.
For more ref , u may check the link : https://math.stackexchange.com/questions/154941/how-to-calculate-the-number-of-possible-connected-simple-graphs-with-n-labelle