Let T be a depth first search tree in an undirected graph G. Vertices u and n…

GATE · 2006 · CS

Let T be a depth first search tree in an undirected graph G. Vertices u and n are leaves of this tree T. The degrees of both u and n in G are at least 2. which one of the following statements is true?

  1. A.

    There must exist a vertex w adjacent to both u and n in G

  2. B.

    There must exist a vertex w whose removal disconnects u and n in G

  3. C.

    There must exist a cycle in G containing u and n

  4. D.

    There must exist a cycle in G containing u and all its neighbours in G.

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Correct answer: D

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