Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Let G = (V,E)be connected undirected edge-wei...
Start Learning for Free
Let G = (V,E) be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:
(I) Minimum Spanning Tree of G is always unique.
(II) Shortest path between any two vertices of G is always unique.
Which of the above statements is/are necessarily true?
- a)(I) only
- b)(II) only
- c)both (I) and (II)
- d)neither (I) nor (II)
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let G = (V,E)be connected undirected edge-weighted graph. The weights ...
> MST is not unique only when edges are not distinct. Here the edges are distinct. Be careful for the keyword
DISTINCT.
DISTINCT.
> Shortest Path can be different even if the edges are distinct. Example is shown below. Shortest path from A
to C is not unique here.
to C is not unique here.
Most Upvoted Answer
Let G = (V,E)be connected undirected edge-weighted graph. The weights ...
Unique Minimum Spanning Tree:
- In a connected undirected edge-weighted graph with distinct edge weights, the Minimum Spanning Tree (MST) is always unique.
- This uniqueness is guaranteed by the cut property, which states that if there are two different MSTs for a graph, they must contain at least one edge with the same weight.
- Since the weights of the edges in the graph are distinct, there can only be one MST.
Non-Unique Shortest Paths:
- While the MST is unique, the shortest path between any two vertices in the graph may not be unique.
- This is because there can be multiple paths with the same minimum weight between two vertices.
- Consider a graph where multiple edges have the same weight, leading to different shortest paths between certain pairs of vertices.
Therefore, the correct answer is option (A) (I) only, as the Minimum Spanning Tree of a connected undirected edge-weighted graph is always unique, but the shortest path between any two vertices may not necessarily be unique.
- In a connected undirected edge-weighted graph with distinct edge weights, the Minimum Spanning Tree (MST) is always unique.
- This uniqueness is guaranteed by the cut property, which states that if there are two different MSTs for a graph, they must contain at least one edge with the same weight.
- Since the weights of the edges in the graph are distinct, there can only be one MST.
Non-Unique Shortest Paths:
- While the MST is unique, the shortest path between any two vertices in the graph may not be unique.
- This is because there can be multiple paths with the same minimum weight between two vertices.
- Consider a graph where multiple edges have the same weight, leading to different shortest paths between certain pairs of vertices.
Therefore, the correct answer is option (A) (I) only, as the Minimum Spanning Tree of a connected undirected edge-weighted graph is always unique, but the shortest path between any two vertices may not necessarily be unique.
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 = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. Can you explain this answer?
Question Description
Let G = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. 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 = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. 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 = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. Can you explain this answer?.
Let G = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. 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 = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. 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 = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. Can you explain this answer?.
Solutions for Let G = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. 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 = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let G = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Let G = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Let G = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let G = (V,E)be connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:(I) Minimum Spanning Tree of G is always unique.(II) Shortest path between any two vertices of G is always unique.Which of the above statements is/are necessarily true?a)(I) onlyb)(II) onlyc)both (I) and (II)d)neither (I) nor (II)Correct answer is option 'A'. 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup