GATE | Gate IT 2007 | Question 3

Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true?
(A) weight (u, v) < 12 (B) weight (u, v) ≤ 12
(C) weight (u, v) > 12
(D) weight (u, v) ≥ 12


Answer: (D)

Explanation:

The minimum weight happens when (S,U) + (U,V) = (S,V)

Else (S,U) + (U,V) >= (S,V)

Given (S,U) = 53, (S,V) = 65

53 + (U,V) >= 63

(U,V) >= 12.

This solution is contributed by Anil Saikrishna Devarasetty

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