GATE 2005
March 12, 2025
GATE 2005
March 12, 2025
GATE 2005
March 12, 2025
GATE 2005
March 12, 2025

GATE 2005

Question 83

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 e 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
Question 83 Explanation: 
Since every edge has distinct edge weights. So, the edge with minimum weight will definitely be present in MST.
Correct Answer: A
Question 83 Explanation: 
Since every edge has distinct edge weights. So, the edge with minimum weight will definitely be present in MST.
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