GATE DA 2025 Set 1 — Question 58
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Programming, Data Structures & Algorithms → Graphs → BFS Shortest Path
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Question
Let be a simple, unweighted, and undirected graph. A subset of the vertices and edges of are shown below.
It is given that is a shortest path between and ; is a shortest path between and ; is a shortest path between and . Which of the following is/are NOT the edges of ?

Correct answer
(A) (b, d); (C) (b, h); (D) (e, g)
Solution
Given shortest paths:
(A) If is an edge, then . This contradicts . So is NOT an edge.
(B) If is an edge, then . This is consistent with . So could be an edge.
(C) If is an edge, then . This contradicts . So is NOT an edge.
(D) If is an edge, then . This contradicts . So is NOT an edge.Thus, (A), (C), and (D) are not edges.
1. is a shortest path between and , so .
2. is a shortest path between and , so .
3. is a shortest path between and , so .
Evaluating the options:(A) If is an edge, then . This contradicts . So is NOT an edge.
(B) If is an edge, then . This is consistent with . So could be an edge.
(C) If is an edge, then . This contradicts . So is NOT an edge.
(D) If is an edge, then . This contradicts . So is NOT an edge.Thus, (A), (C), and (D) are not edges.
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