Let G(V, E) be a simple undirected graph with n > 1 vertices. The complement of G, denoted G, is the subgraph of Kn consisting of the n vertices of G and all edges that are not in G. We say that G is auto-complimentary if G is isomorphic to G. (a) If G is auto-complimentary, how many edges does it have? (b) Prove that if G is auto-complimentary then either n = 4k or n = 4k + 1, for some positive integer k. (c) Find two examples of auto-complimentary graphs for both n = 4 and n = 5.