Problem 7 [15 points] A dominating set S is a subset of vertices of a graph G such that every vertex not in S is adjacent to at least one vertex in S. Let DOMINATING-SET = {(G, k G is a graph that has a dominating set with k vertices) Prove that DOMINATING-SET E NP. [Hint: Construct a nondeterministic TM that decides DOMINATING-SET in polyonimial time and show that your construc- tion is correct. Alternatively, construct a deterministic TM that verifies DOMINATING- SET in polyonimial time.]