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Let T be a depth first search tree in an undirected graph G. Vertices u and n are leaves of this tree T. The degrees of both u and n 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 n in G
  • b)
    There must exist a vertex w whose removal disconnects u and n in G
  • c)
    There must exist a cycle in G containing u and n
  • 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?
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Let T be a depth first search tree in an undirected graph G. Vertices ...
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Let T be a depth first search tree in an undirected graph G. Vertices ...
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Let T be a depth first search tree in an undirected graph G. Vertices ...
Understanding the Depth First Search Tree
In a depth first search (DFS) tree T, leaves represent vertices that have no children in the tree. In this case, both u and n are leaves, meaning that they were the last vertices visited in their respective branches of the DFS.
Vertex Degrees and Implications
- Both u and n have degrees of at least 2 in the original graph G.
- This implies that there are at least two edges connected to each vertex, allowing u and n to connect to other vertices apart from those in the DFS tree.
Analyzing the Statements
- Statement A: "There must exist a vertex w adjacent to both u and n in G."
- Not necessarily true as u and n could connect to completely different sets of vertices.
- Statement B: "There must exist a vertex w whose removal disconnects u and n in G."
- This is also not guaranteed. The removal of a single vertex does not ensure disconnection.
- Statement C: "There must exist a cycle in G containing u and n."
- While possible, it is not guaranteed as they may be connected differently.
- Statement D: "There must exist a cycle in G containing u and all its neighbors in G."
- Correct Statement: Since u is a leaf in the DFS tree but has a degree of at least 2, it must connect to other vertices. These neighbors can potentially connect to each other or n, forming a cycle.
Conclusion
Thus, the existence of a cycle involving u and all its neighbors is ensured by their connections, validating option D as the correct answer.
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Let T be a depth first search tree in an undirected graph G. Vertices u and n are leaves of this tree T. The degrees of both u and n 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 n in Gb)There must exist a vertex w whose removal disconnects u and n in Gc)There must exist a cycle in G containing u and nd)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?
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Let T be a depth first search tree in an undirected graph G. Vertices u and n are leaves of this tree T. The degrees of both u and n 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 n in Gb)There must exist a vertex w whose removal disconnects u and n in Gc)There must exist a cycle in G containing u and nd)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? 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 T be a depth first search tree in an undirected graph G. Vertices u and n are leaves of this tree T. The degrees of both u and n 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 n in Gb)There must exist a vertex w whose removal disconnects u and n in Gc)There must exist a cycle in G containing u and nd)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? covers all topics & solutions for Computer Science Engineering (CSE) 2024 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 n are leaves of this tree T. The degrees of both u and n 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 n in Gb)There must exist a vertex w whose removal disconnects u and n in Gc)There must exist a cycle in G containing u and nd)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?.
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