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GATE 2015 CS (CS2) – Question 62

Engineering Mathematics · Discrete Mathematics: Graphs (Connectivity, Matching, Colouring) · 2 marks · Multiple choice

A bridge is an edge whose removal disconnects a connected graph. Which is true?

  1. A tree has no bridges
  2. A bridge cannot be part of a simple cycle
  3. Every edge of a clique of size at least 3 is a bridge
  4. A graph with bridges cannot have a cycle

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Show answer and explanation

Correct answer: (B) A bridge cannot be part of a simple cycle

Explanation

If an edge lies on a cycle, the rest of that cycle still connects its endpoints after removal, so it cannot be a bridge. Thus B. Every tree edge is a bridge; clique edges lie on cycles; and a graph may contain a cycle with a bridge leading to another component.

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