Algorithm Analysis Graphs proof

I would be very grateful if you could explain it step by step.

Thanks in advance.

A dominating set for an undirected graph 9 = (V, E) is a subset DSV of vertices such that for every vertex i e V, we have: ie D, or i is adjacent to at least one member of D. Notice that finding an arbitrary dominating set for a given graph is trivial, since the set of ver- tices constitutes as a dominating set. The real challenge is finding a small dominating set. The domination number y(9) of a graph 9 is defined as the number of vertices in a smallest dominating set for 9. In this question you are asked to prove that the domination number of a graph is not too big", i.e., no more than half of the number of vertices. Precisely, you are asked to prove the following: For any undirected and connected graph G = (V, E), we have y(951)