Let G be a connected, undirected graph, and let V be the set of all vertices in G. Define a relation R on V as follows: for any vertices a, b = V, a R b if there a path from a to b with an even number of edges. (A path may use the same edge more than once.) Prove that R is an equivalence relation. Suppose the equivalence relation of Exercise 25 is defined on the vertices of the following graph. What are the equivalence classes? b a g 00 d

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