(a) Model the following situation a graphs. Draw the graph, and give the corresponding adjacency matrix. (b) Alfred and Brenda are friends. Alfred is also friends with Catherine and Dylan. Brenda, Catherine and Eric are all friends of each other. Either draw a graph with the following specified properties, or explain why no such graph exists: A simple graph with five vertices with degrees 2, 3, 3, 3, and 5. (c) Consider the following graph. If there is ever a decision between multiple neighbor nodes in the BFS (Breadth First Search) or DFS (Depth First Search) algorithms, assume we always choose the letter closest to the beginning of the alphabet first. (c.1) In what order will the nodes be visited using a Breadth First Search? (c.2) In what order will the nodes be visited using a Depth First Search? (d) Show the ordering of vertices produced by the topological sort algorithm given in class when it is run on the following DAG.