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GATE CSE 2026 Session 1 Q49: Cycle and cut properties of MSTs with distinct weights

Question

Let G(V,E)G(V, E) be a simple, undirected, edge-weighted graph with unique edge weights. Which of the following statements about the minimum spanning trees (MST) of GG is/are true?

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Answer: A, D (official GATE 2026 final answer key)

Concept used: Cycle property (heaviest edge on a cycle is excluded) and cut property (lightest edge across a cut is included).

First step: Apply the cut property to the cut ({v},V∖{v})(\{v\}, V \setminus \{v\}); for C, think of a leaf vertex whose only edge is heavy.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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