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Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the MST of G is/are true? 
  • a)
    Suppose S⊆V be such that S ≠ θ and S ≠ V. Consider the edge with min weight such that one of its vertices is in S and the other in V\S. Such an edge will always be part of any MST of G.
  • b)
    G can have multiple spanning trees.
  • c)
    One or both the edges with the third smallest and the fourth-smallest edges are part of any MST of G. 
  • d)
    The edge with the second-smallest weight is always part of any MST of G.
Correct answer is option 'A,C,D'. Can you explain this answer?
Most Upvoted Answer
Consider a simple undirected weighted graph G, all of whose edge weigh...
The smallest edge is always part of the MST. The graph does not have multiple spanning trees, as all the edge weights are unique. The second and third-smallest edge will be part of the MST if the number of vertices are greater than n > 3 and 4 respectively.
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Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the MST of G is/are true?a)Suppose S⊆V be such that S ≠θ and S ≠ V. Consider the edge with min weight such that one of its vertices is in S and the other in V\S. Such an edge will always be part of any MST of G.b)G can have multiple spanning trees.c)One or both the edges with the third smallest and the fourth-smallest edges are part of any MST of G.d)The edge with the second-smallest weight is always part of any MST of G.Correct answer is option 'A,C,D'. Can you explain this answer?
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Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the MST of G is/are true?a)Suppose S⊆V be such that S ≠θ and S ≠ V. Consider the edge with min weight such that one of its vertices is in S and the other in V\S. Such an edge will always be part of any MST of G.b)G can have multiple spanning trees.c)One or both the edges with the third smallest and the fourth-smallest edges are part of any MST of G.d)The edge with the second-smallest weight is always part of any MST of G.Correct answer is option 'A,C,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 Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the MST of G is/are true?a)Suppose S⊆V be such that S ≠θ and S ≠ V. Consider the edge with min weight such that one of its vertices is in S and the other in V\S. Such an edge will always be part of any MST of G.b)G can have multiple spanning trees.c)One or both the edges with the third smallest and the fourth-smallest edges are part of any MST of G.d)The edge with the second-smallest weight is always part of any MST of G.Correct answer is option 'A,C,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 Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the MST of G is/are true?a)Suppose S⊆V be such that S ≠θ and S ≠ V. Consider the edge with min weight such that one of its vertices is in S and the other in V\S. Such an edge will always be part of any MST of G.b)G can have multiple spanning trees.c)One or both the edges with the third smallest and the fourth-smallest edges are part of any MST of G.d)The edge with the second-smallest weight is always part of any MST of G.Correct answer is option 'A,C,D'. Can you explain this answer?.
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