Minimum degree of an vertex is 0 so there is possibility of 0 edges.
If you are asking minimum number of edge in an connected graph then.
Least number of edges such that graph can be connected is simply n-1
Least number of edges to ensure that graph must be connected is $\frac{(n-1)(n-2)}{2}$+1 or ^{n-1}C_{2}+1
Given equation in question seems to be ambiguous because there is no proper definition of min what is min referred as?