Let G be an undirected graph. Consider a depth-first traversal of G, and let T…

2000

Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true?

  1. A.

    {u, v} must be an edge in G, and u is a descendant of v in T

  2. B.

    {u, v} must be an edge in G, and v is a descendant of u in T

  3. C.

    If {u, v} is not an edge in G then u is a leaf in T

  4. D.

    If {u, v} is not an edge in G then u and v must have the same parent in T

Attempted by 19 students.

Show answer & explanation

Correct answer: C

Provide a detailed explanation of DFS tree properties regarding the relationship between vertex u and the first new vertex v.

A video solution is available for this question — log in and enroll to watch it.

Explore the full course: Gate Guidance By Sanchit Sir