Let ๐บ be a directed graph and ๐‘‡ a depth first search (DFS) spanning tree inโ€ฆ

GATE ยท 2024 ยท CS ยท Set 1 ยท Computer Science & IT

Let ๐บ be a directed graph and ๐‘‡ a depth first search (DFS) spanning tree in ๐บ that is rooted at a vertex ๐‘ฃ. Suppose ๐‘‡ is also a breadth first search (BFS) tree in ๐บ, rooted at ๐‘ฃ. Which of the following statements is/are TRUE for every such graph ๐บ and tree ๐‘‡ ?ย ย ย ย 

  1. A.

    There are no back-edges in ๐บ with respect to the tree ๐‘‡

  2. B.

    There are no cross-edges in ๐บ with respect to the tree ๐‘‡

  3. C.

    There are no forward-edges in ๐บ with respect to the tree ๐‘‡

  4. D.

    The only edges in ๐บ are the edges in ๐‘‡

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