Algorithms | Graph Traversals | Question 12

If the DFS finishing time f[u] > f[v] for two vertices u and v in a directed graph G, and u and v are in the same DFS tree in the DFS forest, then u is an ancestor of v in the depth first tree. (Source http://courses.csail.mit.edu/6.006/oldquizzes/solutions/q2-f2007-sol.pdf)
(A) True
(B) False


Answer: (B)

Explanation: In a graph with three nodes, r u and v, with edges (r; u) and (r; v), and r is the starting point for the DFS, u and v are siblings in the DFS tree, neither as the ancestor of the other.

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