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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? (GATE CS 2000)
  • a)
    {u,v} must be an edge in G, and u is a descendant of v in T
  • b)
    {u,v} must be an edge in G, and v is a descendant of u in T
  • c)
    If {u,v} is not an edge in G then u is a leaf in T
  • d)
    If {u,v} is not an edge in G then u and v must have the same parent in T
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let G be an undirected graph. Consider a depth-first traversal of G, a...
In DFS, if 'v' is visited after 'u', then one of the following is true.
1) (u, v) is an edge.
2) 'u' is a leaf node.
In DFS, after visiting a node, we first recur for all unvisited children. If there are no unvisited children (u is leaf), then control goes back to parent and parent then visits next unvisited children.
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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? (GATE CS 2000)a){u,v} must be an edge in G, and u is a descendant of v in Tb){u,v} must be an edge in G, and v is a descendant of u in Tc)If {u,v} is not an edge in G then u is a leaf in Td)If {u,v} is not an edge in G then u and v must have the same parent in TCorrect answer is option 'C'. Can you explain this answer?
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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? (GATE CS 2000)a){u,v} must be an edge in G, and u is a descendant of v in Tb){u,v} must be an edge in G, and v is a descendant of u in Tc)If {u,v} is not an edge in G then u is a leaf in Td)If {u,v} is not an edge in G then u and v must have the same parent in TCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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? (GATE CS 2000)a){u,v} must be an edge in G, and u is a descendant of v in Tb){u,v} must be an edge in G, and v is a descendant of u in Tc)If {u,v} is not an edge in G then u is a leaf in Td)If {u,v} is not an edge in G then u and v must have the same parent in TCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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? (GATE CS 2000)a){u,v} must be an edge in G, and u is a descendant of v in Tb){u,v} must be an edge in G, and v is a descendant of u in Tc)If {u,v} is not an edge in G then u is a leaf in Td)If {u,v} is not an edge in G then u and v must have the same parent in TCorrect answer is option 'C'. Can you explain this answer?.
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