can you analyze the complexity of the algorithms?

Question 1: Let vi, v2..., Un be an ordering of the vertices of an undirected graph G(V, E) on a line. Let N.(u) be the neighbors of v that appear after v in the line. The ordering is called a perfect elimination sequence if for every v, N. (v) is a clique (a clique is a graph such that an two vertices are neighbors). 1. Consider the following algorithm: While there are still vertices in the line, take the first (non deleted) vertex u in the line. Define a set uU N.(u) and remove this set and any edge touching a vertex from this set, from the graph. Then iterate. Show that the above algorithm decomposes the graph into disjoint cliques. 2. Say that the above algorithm gives q cliques. Show that the maximum indepen- dent set in the graph has size at most q. 3. Show that the maximum in dependent set has size at least q. 4. Show that that the algorithm find a maximum independent set in the graph