GATE CS 2015 Set 3 — Question 55
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumTrees & Spanning TreesGraph Theory (Math)Engineering MathematicsGreedy AlgorithmsAlgorithms
Algorithms → Graph Theory (Math) → Trees & Spanning Trees
Last updated
Question
Let be a connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of is 500. When the weight of each edge of is increased by five, the weight of a minimum spanning tree becomes __________.
Correct answer
995 to 995
Solution
A Minimum Spanning Tree (MST) of a graph with vertices always has edges.
Here, , so the MST has edges.When the weight of every edge in the graph is increased by a constant , the structure of the MST remains the same (since the relative order of edge weights does not change). The weight of the new MST will be the old weight plus times the number of edges in the MST.New Weight = Old Weight + (Number of edges in MST Increase per edge)
New Weight =
New Weight = .
Here, , so the MST has edges.When the weight of every edge in the graph is increased by a constant , the structure of the MST remains the same (since the relative order of edge weights does not change). The weight of the new MST will be the old weight plus times the number of edges in the MST.New Weight = Old Weight + (Number of edges in MST Increase per edge)
New Weight =
New Weight = .
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 Theory (Math)
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…