GATE DA 2026 Set 1 — Question 40
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Programming, Data Structures & Algorithms → Graphs → Graph Traversals (BFS, DFS)
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Question
Consider a directed graph , where is the finite set of vertices and is the set of directed edges between the vertices. may contain cycles but there is no self-loop. Further, may not be strongly connected.Let be the graph obtained by reversing the directions of all the edges in without changing the set of vertices.Assume that Breadth First Search (BFS) or Depth First Search (DFS) from any given vertex of a graph visits only the reachable vertices from in that graph.Which of the following statements must always be true, regardless of the structure of ?
Correct answer
(D) If u is a reachable vertex in the DFS of G from v, then v is also a reachable vertex in the BFS of G^R from u.
Solution
Let denote the set of vertices reachable from in graph . The problem states that BFS/DFS from visits exactly .Option (D) states: "If is a reachable vertex in the DFS of from , then is also a reachable vertex in the BFS of from ."
1. is reachable in DFS of from there exists a directed path from to in : .
2.In , all edge directions are reversed. Therefore, the path in corresponds to a path in .
3.This implies that is reachable from in .
4.Since BFS from in visits all vertices reachable from , it must visit .
Thus, statement (D) is always true.Continue learning with Success Tracker
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