a) Suppose a directed graph has k nodes, where there are two "special" nodes. One has an edge from itself to every non-special node and the other has an edge from every non-special node to itself. There are no other edges at all in the graph. i. Draw the graph (using circles and arrows) assuming k = 4. ii. Draw an adjacency list representation of the graph assuming k = 4. iii. In terms of k, exactly how many edges are in the graph? iv. Is this graph dense or sparse? v. In terms of k (if k is relevant), exactly how many correct results for topological sort that does this graph have?

Note that for parts (iii),(iv), and (v), your answer should be in terms of an arbitrary k, not assuming k = 4.