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Let S and t be two vertices in a undirected graph G=(V,E) having distinct positive edge weights. Let [X,Y] be a partition of  V such that  s ∈ X and t ∈ Y . Consider the edge  having the minimum  weight amongst all those edges that have one vertex in X and one vertex in Y
The edge e must definitely belong to:.
  • a)
    the minimum weighted spanning tree of G
  • b)
    the weighted shortest path from s to t
  • c)
    each path from s to t
  • d)
    the weighted longest path from s to t
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let S and t be two vertices in a undirected graph G=(V,E)having distin...
For 82a The answer should be Option A because edge 'e' is the lightest safe edge connecting X and Y so the minimum
spanning tree of G must contain 'e' (Greedy and optimal choice).
While B might seem correct but it is not always true. One such case is when G is not connected therefore there might not
be any path between 's' and 't'.
Since the question is about definitely true B is incorrect and A is the only correct option
Lets say AC =1 CD = 2 BD = 3 and AB=4
Then if s= A and t= B then AC is the lightest edge crossing X and Y where X = { A } and Y = { C, B, D}
But clearly AC is not on the shortest path from A to B. The shortest path is AB = 4.
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Most Upvoted Answer
Let S and t be two vertices in a undirected graph G=(V,E)having distin...
Explanation:

Minimum Weighted Spanning Tree:
- The edge e with the minimum weight amongst all edges connecting X and Y will definitely be a part of the minimum weighted spanning tree of the graph G.
- This is because in a minimum weighted spanning tree, the sum of the weights of the edges is minimized while still connecting all vertices in the graph.
- As e is the minimum weight edge connecting X and Y, it will be necessary for the spanning tree to connect these two partitions with the minimum possible weight.

Weighted Shortest Path from s to t:
- The edge e will also be a part of the weighted shortest path from s to t.
- This is because in a shortest path, we aim to minimize the total weight of the path from s to t.
- As e is the minimum weight edge connecting X and Y, it will be included in the shortest path to minimize the total weight from s to t.

Each Path from s to t:
- The edge e may not necessarily belong to each path from s to t.
- While it will be a part of the minimum weighted spanning tree and the weighted shortest path from s to t, it may not be present in all possible paths from s to t.
- Paths that do not include e may have a higher total weight compared to those that include e.

Weighted Longest Path from s to t:
- The edge e will definitely not be a part of the weighted longest path from s to t.
- In the longest path, we aim to maximize the total weight of the path from s to t.
- As e is the minimum weight edge connecting X and Y, it will not be included in the longest path as it minimizes the total weight.
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Let S and t be two vertices in a undirected graph G=(V,E)having distinct positive edge weights. Let [X,Y]be apartition of Vsuch that s ∈ X and t∈ Y. Consider the edge having the minimum weight amongst all those edges thathave one vertex in X and one vertex in YThe edge e must definitely belong to:.a)the minimum weighted spanning tree of Gb)the weighted shortest path from s to tc)each path from s to td)the weighted longest path from s to tCorrect answer is option 'A'. Can you explain this answer?
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Let S and t be two vertices in a undirected graph G=(V,E)having distinct positive edge weights. Let [X,Y]be apartition of Vsuch that s ∈ X and t∈ Y. Consider the edge having the minimum weight amongst all those edges thathave one vertex in X and one vertex in YThe edge e must definitely belong to:.a)the minimum weighted spanning tree of Gb)the weighted shortest path from s to tc)each path from s to td)the weighted longest path from s to tCorrect answer is option 'A'. 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 S and t be two vertices in a undirected graph G=(V,E)having distinct positive edge weights. Let [X,Y]be apartition of Vsuch that s ∈ X and t∈ Y. Consider the edge having the minimum weight amongst all those edges thathave one vertex in X and one vertex in YThe edge e must definitely belong to:.a)the minimum weighted spanning tree of Gb)the weighted shortest path from s to tc)each path from s to td)the weighted longest path from s to tCorrect answer is option 'A'. 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 S and t be two vertices in a undirected graph G=(V,E)having distinct positive edge weights. Let [X,Y]be apartition of Vsuch that s ∈ X and t∈ Y. Consider the edge having the minimum weight amongst all those edges thathave one vertex in X and one vertex in YThe edge e must definitely belong to:.a)the minimum weighted spanning tree of Gb)the weighted shortest path from s to tc)each path from s to td)the weighted longest path from s to tCorrect answer is option 'A'. Can you explain this answer?.
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