GATE DA 2024 Set 1 — Question 14
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Programming, Data Structures & Algorithms → Graphs → Graph Traversals (BFS, DFS)
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Question
Consider performing depth-first search (DFS) on an undirected and unweighted graph starting at vertex . For any vertex in , is the length of the shortest path from to . Let be an edge in such that . If the edge is explored first in the direction from to during the above DFS, then becomes a ______ edge.
Correct answer
(A) tree
Solution
In a DFS on an undirected graph, every edge is classified as either a tree edge or a back edge. There are no forward or cross edges.The statement says the edge is explored first in the direction from to . This implies that when the DFS process at vertex examines the edge , the vertex has not yet been visited. If had been visited earlier (e.g., as an ancestor of ), the edge would have been explored from to first (as a tree edge if was unvisited, or a back edge if was visited). Since it is explored from to first, must be unvisited at that moment. Therefore, the DFS traverses from to , making a tree edge.The condition (shortest path distances) is consistent with a tree edge moving away from the source, but the key determinant is the exploration order.
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