In graph theory, a dominating set for a graph G = (V, E) is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number v(G) is the number of vertices in a smallest dominating set for G. The dominating set problem concerns testing whether v(G) K for a given graph G and input K. Prove that the dominating set problem is NP-complete via a polynomial reduction from vertex cover problem to it.