An adjacency matrix representation of a graph with V vertices and E edges requires O(V^2) space, as it uses a V x V matrix. An adjacency list representation requires O(V+E) space, as it stores a list of neighbors for each vertex. For a sparse graph, a topological sort should use an adjacency list representation because it uses less space than the adjacency matrix representation.

1. Data structure
2. (10 points) If a graph has V vertices and E edges, what is the space requirement (big-O
notation is fine) for representing this graph as an adjacency matrix? As an adjacency list? If we
perform a topological sort on a sparse graph, which representation should we use and why?