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  3. let g v e be a graph recall from class...

Question: let g v e be a graph recall from class...

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Let G -(V, E) be a graph. Recall from class that the complement of G, denoted G, is the graph that has vertex set V in which two vertices are adjacent if and only if they are not adjacent in G. ie. E(G) {uv | uvE E(G), u, v € V). Also recall that G is called self-complementary if G is isomorphic to (a) Is there a graph G on 5 vertices such that G and G are both bipartite? If not, explain why not. If so, give an example of such a graph G (b) Prove that if G is self-complementary and IV(G)-n, then n -4k or n 4k1 for some positive integer k. Hint: We calculated E(G)l for self-complementary graphs in class.

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