Isn't this trivial? If G and H have the same shape, then their complements must have the same shape... I don't know a way to "show" it. --Mkorb 18:33, 12 November 2008 (UTC)
I think you need to actually construct a function that produces an isomorphism between the complement of G and the complement of H. Consider the function that does the "opposite" of the function that assigns the isomorphism from G to H.
Consider how to describe the complement of a graph in terms of G, H and their respective complete graphs. Then show that they are isomorphic.
--ysuo
