b) Suppose a directed graph has k nodes, where each node corresponds to a number (1, 2, ..., k) and there is an edge from node i to node j if and only if i mod 2 j mod 2 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 assuming k is even? 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