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

(a) 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 < j. i. Draw the graph (using circles and arrows) assuming k = 4.

ii. Draw an adjacency matrix 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