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  3. 4 let g ve be defined as follows v set...

Question: 4 let g ve be defined as follows v set...

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4. Let G- (V,E) be defined as follows. V set of all subsets of S, where S 1,2,3,...,6) Note that this means V26. For v1, v2 E V, v1U2 E E iff vi U v2- S. For example, if v 1,2,5} and v2-11,3, 4,6], then viv2E E (a) For v-[1), find deg(v). (b) For v-[1,21, find deg(v) (c) Find |E] 5. 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. i.e. E(C) {uv | uv Ģ E(G), u, v є V). Also recall that G is called self-complementary if G is isomorphic to G. (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 |V (G) -n, then n - 4k or n - 4k + 1 for some positive integer k. Hint: We calculated E(G)| for self-complementary graphs in class.

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