GATE CSE 2025 Session 1 Q18: Shortest distances in a graph versus its MST

Algorithms
1 mark
MCQ
−1/3 if wrong

Let $G$ be any undirected graph with positive edge weights, and $T$ be a minimum spanning tree of $G$ . For any two vertices, $u$ and $v$ , let $d_1(u, v)$ and $d_2(u, v)$ be the shortest distances between $u$ and $v$ in $G$ and $T$ , respectively. Which ONE of the options is CORRECT for all possible $G$ , $T$ , $u$ and $v$ ?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: B (official GATE 2025 final answer key)

Concept used: An MST is a subgraph, and removing edges can never shorten a shortest path.

First step: The tree path from $u$ to $v$ is also a path in $G$ , so the shortest path in $G$ is at most as long.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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GATE CSE 2025 Session 1 Q18: Shortest distances in a graph versus its MST

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