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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 statement is always true?
- 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 and v must have the same parent in T
- d)If {u, v} is not an edge in G then u is a leaf in T
Correct answer is option 'D'. Can you explain this answer?
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Let G be an undirected graph. Consider a depth-first traversal of G, a...
Correct option is C. If {u, v} is not an edge in G then u is a leaf in T
Most Upvoted Answer
Let G be an undirected graph. Consider a depth-first traversal of G, a...
Explanation:
In a depth-first traversal of an undirected graph G, we start at a given vertex and explore as far as possible along each branch before backtracking.
Depth-First Search (DFS):
- Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.
- The algorithm starts at a specified vertex and explores as far as possible along each branch before backtracking.
- It uses a stack to remember which vertices to visit next.
Depth-First Search Tree (T):
- The depth-first search tree T is a directed graph formed during the depth-first traversal of the original undirected graph G.
- In T, each vertex is visited only once.
- T contains all the vertices of G and a subset of the edges of G.
First New Vertex (v) Visited After u:
- Let u be a vertex in G and v be the first new (unvisited) vertex visited after visiting u in the traversal.
- This means that v is the next vertex encountered in the depth-first search after visiting u.
Statement Options:
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 and v must have the same parent in T.
d) If {u, v} is not an edge in G then u is a leaf in T.
Analysis of Statement Options:
a) {u, v} must be an edge in G, and u is a descendant of v in T.
- This statement is not always true because {u, v} does not necessarily have to be an edge in G.
- It is possible for v to be a vertex that is not connected to u by an edge in G.
b) {u, v} must be an edge in G, and v is a descendant of u in T.
- This statement is not always true because {u, v} does not necessarily have to be an edge in G.
- It is possible for v to be a vertex that is not connected to u by an edge in G.
c) If {u, v} is not an edge in G then u and v must have the same parent in T.
- This statement is not always true because u and v can have different parents in T.
- It is possible for u and v to be connected in T through another path that does not involve their immediate parent-child relationship.
d) If {u, v} is not an edge in G then u is a leaf in T.
- This statement is always true because if {u, v} is not an edge in G, it means that u and v are not connected in G.
- In the depth-first traversal, after visiting u, if v is the first new vertex encountered, it means that there are no more unvisited vertices connected to u.
- Therefore, u does not have any outgoing edges in T and is a leaf in T.
Conclusion:
The correct answer is option 'D'. If {u, v} is not an edge in G, then u is a leaf in T.
In a depth-first traversal of an undirected graph G, we start at a given vertex and explore as far as possible along each branch before backtracking.
Depth-First Search (DFS):
- Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.
- The algorithm starts at a specified vertex and explores as far as possible along each branch before backtracking.
- It uses a stack to remember which vertices to visit next.
Depth-First Search Tree (T):
- The depth-first search tree T is a directed graph formed during the depth-first traversal of the original undirected graph G.
- In T, each vertex is visited only once.
- T contains all the vertices of G and a subset of the edges of G.
First New Vertex (v) Visited After u:
- Let u be a vertex in G and v be the first new (unvisited) vertex visited after visiting u in the traversal.
- This means that v is the next vertex encountered in the depth-first search after visiting u.
Statement Options:
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 and v must have the same parent in T.
d) If {u, v} is not an edge in G then u is a leaf in T.
Analysis of Statement Options:
a) {u, v} must be an edge in G, and u is a descendant of v in T.
- This statement is not always true because {u, v} does not necessarily have to be an edge in G.
- It is possible for v to be a vertex that is not connected to u by an edge in G.
b) {u, v} must be an edge in G, and v is a descendant of u in T.
- This statement is not always true because {u, v} does not necessarily have to be an edge in G.
- It is possible for v to be a vertex that is not connected to u by an edge in G.
c) If {u, v} is not an edge in G then u and v must have the same parent in T.
- This statement is not always true because u and v can have different parents in T.
- It is possible for u and v to be connected in T through another path that does not involve their immediate parent-child relationship.
d) If {u, v} is not an edge in G then u is a leaf in T.
- This statement is always true because if {u, v} is not an edge in G, it means that u and v are not connected in G.
- In the depth-first traversal, after visiting u, if v is the first new vertex encountered, it means that there are no more unvisited vertices connected to u.
- Therefore, u does not have any outgoing edges in T and is a leaf in T.
Conclusion:
The correct answer is option 'D'. If {u, v} is not an edge in G, then u is a leaf in T.
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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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. Can you explain this answer?.
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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. Can you explain this answer?, a detailed solution 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of 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 statement is always true?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 and v must have the same parent in Td)If {u, v} is not an edge in G then u is a leaf in TCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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