Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Let G be connected undirected graph of 100 ve...
Start Learning for Free
Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.
- a)1000
- b)995
- c)2000
- d)1995
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let G be connected undirected graph of 100 vertices and 300 edges. The...
Since there are 100 vertices, there must be 99 edges in Minimum Spanning Tree (MST).
When weight of every edge is increased by 5, the increment in weight of MST is = 99 * 5 = 495
So new weight of MST is 500 + 495 which is 995
Most Upvoted Answer
Let G be connected undirected graph of 100 vertices and 300 edges. The...
Since there are 100 vertices, there must be 99 edges in Minimum Spanning Tree (MST). When weight of every edge is increased by 5, the increment in weight of MST is = 99 * 5 = 495 So new weight of MST is 500 + 495 which is 995
Free Test
FREE
| Start Free Test |
Community Answer
Let G be connected undirected graph of 100 vertices and 300 edges. The...
Introduction:
In this question, we are given a connected undirected graph G with 100 vertices and 300 edges. We know that the weight of a minimum spanning tree (MST) of G is 500. We are asked to find the weight of the MST when the weight of each edge of G is increased by five.
Explanation:
To solve this problem, we need to understand the concept of a minimum spanning tree and how it is affected by changes in edge weights.
1. Minimum Spanning Tree (MST):
A minimum spanning tree of a connected undirected graph is a tree that spans all the vertices of the graph and has the minimum total weight among all possible spanning trees. The weight of a tree is the sum of the weights of its edges.
2. Effect of Increasing Edge Weights:
When the weight of each edge in the graph is increased by the same amount, it does not change the relative ordering of the edge weights. In other words, the edges that were previously the lightest will still be the lightest after the weight increase.
3. Effect on Minimum Spanning Tree:
Since the relative ordering of the edge weights remains the same, the minimum spanning tree will still contain the same edges as before, but with increased weights. The overall weight of the minimum spanning tree will be equal to the sum of the increased weights of the edges.
4. Calculation:
In the given graph, the weight of the minimum spanning tree (MST) is 500. When the weight of each edge is increased by five, the weight of the MST becomes 500 + 5 * 300 = 500 + 1500 = 2000.
Conclusion:
Therefore, the weight of the minimum spanning tree after increasing the weight of each edge by five is 2000. Hence, option (c) 2000 is the correct answer.
In this question, we are given a connected undirected graph G with 100 vertices and 300 edges. We know that the weight of a minimum spanning tree (MST) of G is 500. We are asked to find the weight of the MST when the weight of each edge of G is increased by five.
Explanation:
To solve this problem, we need to understand the concept of a minimum spanning tree and how it is affected by changes in edge weights.
1. Minimum Spanning Tree (MST):
A minimum spanning tree of a connected undirected graph is a tree that spans all the vertices of the graph and has the minimum total weight among all possible spanning trees. The weight of a tree is the sum of the weights of its edges.
2. Effect of Increasing Edge Weights:
When the weight of each edge in the graph is increased by the same amount, it does not change the relative ordering of the edge weights. In other words, the edges that were previously the lightest will still be the lightest after the weight increase.
3. Effect on Minimum Spanning Tree:
Since the relative ordering of the edge weights remains the same, the minimum spanning tree will still contain the same edges as before, but with increased weights. The overall weight of the minimum spanning tree will be equal to the sum of the increased weights of the edges.
4. Calculation:
In the given graph, the weight of the minimum spanning tree (MST) is 500. When the weight of each edge is increased by five, the weight of the MST becomes 500 + 5 * 300 = 500 + 1500 = 2000.
Conclusion:
Therefore, the weight of the minimum spanning tree after increasing the weight of each edge by five is 2000. Hence, option (c) 2000 is the correct answer.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer?
Question Description
Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer?.
Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer?.
Solutions for Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes ________.a)1000b)995c)2000d)1995Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup