GATE CS 2015 Set 2 — Question 62
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67EasyConnectivityGraph Theory (Math)Engineering MathematicsArticulation Points & BridgesGraph AlgorithmsAlgorithms
Algorithms → Graph Algorithms → Articulation Points & Bridges
Last updated
Question
In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is true?
Correct answer
(B) A bridge cannot be part of a simple cycle
Solution
Option (A) is false: In a tree, every edge is a bridge because removing any edge disconnects the tree.
Option (B) is true: An edge is a bridge if and only if it does not lie on any cycle. If it were on a cycle, removing it would leave another path between and (the rest of the cycle), so the graph would remain connected.
Option (C) is false: In a clique of size , every edge is part of a triangle (cycle), so no edge is a bridge.
Option (D) is false: A graph can have both bridges and cycles (e.g., two disjoint cycles connected by a single edge).
Option (B) is true: An edge is a bridge if and only if it does not lie on any cycle. If it were on a cycle, removing it would leave another path between and (the rest of the cycle), so the graph would remain connected.
Option (C) is false: In a clique of size , every edge is part of a triangle (cycle), so no edge is a bridge.
Option (D) is false: A graph can have both bridges and cycles (e.g., two disjoint cycles connected by a single edge).
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Graph Algorithms
2026 Set 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…