Let ๐บ(๐‘‰,๐ธ) be a simple, undirected, edge-weighted graph with unique edgeโ€ฆ

PYQ GATE 2026

Let ๐บ(๐‘‰,๐ธ) be a simple, undirected, edge-weighted graph with unique edge weights. Which of the following statements about the minimum spanning trees (MST) of ๐บ is/are true?

  1. A.

    In every cycle ๐ถ of ๐บ, the edge with the largest weight in ๐ถ is not in any MST

  2. B.

    In every cycle ๐ถ of ๐บ, the edge with the smallest weight in ๐ถ is in every MST

  3. C.

    For every vertex ๐‘ฃ โˆˆ๐‘‰, the edge with the largest weight incident on ๐‘ฃ is not in any MST

  4. D.

    For every vertex ๐‘ฃ โˆˆ๐‘‰, the edge with the smallest weight incident on ๐‘ฃ is in every MST

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