GATE CS 2019 Set 1 — Question 48

MCQ+2 / -0.67MediumTrees & Spanning TreesGraph Theory (Math)Engineering MathematicsKruskal's MSTGreedy AlgorithmsAlgorithmsPrim's MST

Algorithms → Graph Theory (Math) → Kruskal's MST

Last updated 5 September 2026

Question

G

Correct answer (C) Both I and II Solution Statement I is correct: If all edge weights in a connected graph are distinct, the Minimum Spanning Tree (MST) is unique. Statement II is correct: A graph has a unique MST if and only if for every cut (a partition of the vertices into two disjoint sets), the edge with the minimum weight crossing the cut is unique. This is a known necessary and sufficient condition for the uniqueness of an MST. Thus, both statements are true. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (C) Both I and II Solution Statement I is correct: If all edge weights in a connected graph are distinct, the Minimum Spanning Tree (MST) is unique. Statement II is correct: A graph has a unique MST if and only if for every cut (a partition of the vertices into two disjoint sets), the edge with the minimum weight crossing the cut is unique. This is a known necessary and sufficient condition for the uniqueness of an MST. Thus, both statements are true.

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