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Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?
- a)There must exist a vertex w adjacent to both u and ν in G
- b)There must exist a vertex w whose removal disconnects u and ν in G
- c)There must exist a cycle in G containing u and ν
- d)There must exist a cycle in G containing u and all its neighbours in G
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let T be a depth first search tree in an undirected graph G. Vertices ...
Consider following graph
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so D is answer.
so D is answer.
Most Upvoted Answer
Let T be a depth first search tree in an undirected graph G. Vertices ...
Statement and Explanation:
The statement is asking which of the given options is true when considering a depth-first search tree T in an undirected graph G, where u and v are leaves with degrees of at least 2 in G.
Option A: There must exist a vertex w adjacent to both u and v in G.
Option B: There must exist a vertex w whose removal disconnects u and v in G.
Option C: There must exist a cycle in G containing u.
Option D: There must exist a cycle in G containing u and all its neighbors in G.
Analysis:
To determine which option is true, let's analyze each option:
Option A: There must exist a vertex w adjacent to both u and v in G.
- This option is not necessarily true because u and v could be leaves connected to different branches in T, making it possible for there not to be a vertex w adjacent to both u and v in G.
Option B: There must exist a vertex w whose removal disconnects u and v in G.
- This option is not necessarily true because u and v could be leaves connected to the same branch in T, and the removal of any vertex would not disconnect u and v in G.
Option C: There must exist a cycle in G containing u.
- This option is not necessarily true because u is a leaf and does not have any outgoing edges in T, so it cannot be part of a cycle in G.
Option D: There must exist a cycle in G containing u and all its neighbors in G.
- This option is true because u and v are leaves with degrees of at least 2 in G. This means that they have at least one neighbor each in G. Since u is a leaf, its only neighbor is v. Therefore, there exists a cycle in G containing u and all its neighbors (which is just v).
Conclusion:
Based on the analysis, the correct answer is option D.
The statement is asking which of the given options is true when considering a depth-first search tree T in an undirected graph G, where u and v are leaves with degrees of at least 2 in G.
Option A: There must exist a vertex w adjacent to both u and v in G.
Option B: There must exist a vertex w whose removal disconnects u and v in G.
Option C: There must exist a cycle in G containing u.
Option D: There must exist a cycle in G containing u and all its neighbors in G.
Analysis:
To determine which option is true, let's analyze each option:
Option A: There must exist a vertex w adjacent to both u and v in G.
- This option is not necessarily true because u and v could be leaves connected to different branches in T, making it possible for there not to be a vertex w adjacent to both u and v in G.
Option B: There must exist a vertex w whose removal disconnects u and v in G.
- This option is not necessarily true because u and v could be leaves connected to the same branch in T, and the removal of any vertex would not disconnect u and v in G.
Option C: There must exist a cycle in G containing u.
- This option is not necessarily true because u is a leaf and does not have any outgoing edges in T, so it cannot be part of a cycle in G.
Option D: There must exist a cycle in G containing u and all its neighbors in G.
- This option is true because u and v are leaves with degrees of at least 2 in G. This means that they have at least one neighbor each in G. Since u is a leaf, its only neighbor is v. Therefore, there exists a cycle in G containing u and all its neighbors (which is just v).
Conclusion:
Based on the analysis, the correct answer is option D.
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Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer?.
Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T. The degrees of both u and ν in G are at least 2. which one of the following statements is true?a)There must exist a vertex w adjacent to both u and ν in Gb)There must exist a vertex w whose removal disconnects u and ν in Gc)There must exist a cycle in G containing u and νd)There must exist a cycle in G containing u and all its neighbours in GCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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