1. The problem statement, all variables and given/known data How many complete bipartite graphs have n vertices? 2. Relevant equations 3. The attempt at a solution I said, let the first bipartition set have x vertices and the second bipartition set have y vertices. So x+y=n. I think that you would do C(n, x)*C(n-x, y)=C(n,x)*C(y,y)=C(n,x) but I feel like this is either wrong or not good since I made x and y up arbitrarily. Help?