00:01
We are given two isomorphic simple graphs, and we're asked to show that their complementary graphs are also isomorphic.
00:12
So suppose that g, which is equal to v1e1, and h is v1, e2, or sorry, v2, e2, are simple graphs such that they are isomorphic, and then follows that we can find function f from v1 to v2 such that f is 1 to 1 and on 2 and we have that an edge uv lies in the set e1 if and only if the edge f of u f of v lies in the set e1 if and only if the edge f of u f of v lies in the set e2.
01:53
Now, the complementary graphs will contain the same set of vertices, but contain all edges not contained in the original graphs.
02:04
So it follows that the complement of g is going to be the pair of v1, and then the complement of e1, and the complement of h is equal to v2, and the complement of e2.
02:34
So, now to prove that these are isomorphic, we're going to take f to be the function from v1 to v2 from earlier...