a) Show that if G is a simple graph with n vertices (where n is a positive integer) and each vertex has degree greater than or equal to (n−1)/2, then the diameter of G is 2 or less. (b) If G is a (not necessarily simple) graph with n vertices where each vertex has degree greater than or equal to (n−1)/2, is the diameter of G necessarily 2 or less? Either prove that the answer to this question is "yes" or give a counterexample.

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