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Let ω be the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weight ω . Which of the following is FALSE?
  • a)
    There is a minimum spanning tree containing e
  • b)
    If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T , all edges have the same weight.
  • c)
    Every minimum spanning tree has an edge of weight ω
  • d)
    e is present in every minimum spanning tree
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let ωbe the minimum weight among all edge weights in an undirecte...
D is the false statement.
A minimum spanning tree must have the edge with the smallest weight (In Kruskal's algorithm we start from the smallest weight edge). So, C is TRUE.
If e is not part of a minimum spanning tree, then all edges which are part of a cycle with e, must have weight ≤ e, as otherwise we can interchange that edge with e and get another minimum spanning tree of lower weight. So, B and A are also TRUE.
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Let ωbe the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weightω . Which of the following is FALSE?a)There is a minimum spanning tree containing eb)If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T , all edges have the same weight.c)Every minimum spanning tree has an edge of weightωd)e is present in every minimum spanning treeCorrect answer is option 'D'. Can you explain this answer?
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Let ωbe the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weightω . Which of the following is FALSE?a)There is a minimum spanning tree containing eb)If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T , all edges have the same weight.c)Every minimum spanning tree has an edge of weightωd)e is present in every minimum spanning treeCorrect 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 ωbe the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weightω . Which of the following is FALSE?a)There is a minimum spanning tree containing eb)If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T , all edges have the same weight.c)Every minimum spanning tree has an edge of weightωd)e is present in every minimum spanning treeCorrect 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 ωbe the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weightω . Which of the following is FALSE?a)There is a minimum spanning tree containing eb)If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T , all edges have the same weight.c)Every minimum spanning tree has an edge of weightωd)e is present in every minimum spanning treeCorrect answer is option 'D'. Can you explain this answer?.
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