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4. (20 pts.) Graph Basics: Give a short answer to each of the questions below. A B E F H (a) Write down the adjacency list representation of the graph above. (b) What is the most number of edges that an undirected graph can have? Give an exact answer in terms of |V], without asymptotic notation. You may assume that there are no parallel edges, i.e. for any two vertices u and v, there is at most one edge {u, v}. (c) For each vertex v; in an undirected graph, let d; be its degree, which is the number of edges incident to it. Show that I, d, must be even. You may assume that there are no self-loops, i.e. edges of the form (u, u). (d) Suppose your boss is trying to solve a problem on a graph, and you present them with two algorithms. The first runs in time (V||E). The second runs in time (Vlog|VD). Your boss is happy you know the running times, but they seem confused as to which one is better. So they ask you to tell them, in plain English, which algorithm will run faster. What do you answer? (e) Suppose instead that the first algorithm runs in time (|E|log|V) and the second runs in (E|log|E]). What do you tell your boss then