GATE CS 2025 Set 1 — Question 64
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Algorithms → Graph Theory (Math) → Kruskal's MST
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Question
The maximum value of such that the edge between the nodes B and C is included in every minimum spanning tree of the given graph is _________ . (answer in integer)
Correct answer
5 to 5
Solution
An edge is included in every minimum spanning tree (MST) of a graph if and only if for every cycle containing , the weight of is strictly less than the maximum weight of the other edges in that cycle.Let's identify the cycles containing the edge (B, C) with weight :
1.Cycle B-C-A-B: The edges are (B, C) with weight , (C, A) with weight 1, and (A, B) with weight 7. For (B, C) to be in every MST, .
2.Cycle B-C-D-B: The edges are (B, C) with weight , (C, D) with weight 8, and (D, B) with weight 3. For (B, C) to be in every MST, .
3.Cycle B-C-A-D-B: The edges are (B, C) with weight , (C, A) with weight 1, (A, D) with weight 6, and (D, B) with weight 3. For (B, C) to be in every MST, .
To satisfy all conditions, must be strictly less than the minimum of these maximums: .The maximum integer value of that satisfies is 5.Continue learning with Success Tracker
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