Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > In a depth-first traversal of a graph G with ...
Start Learning for Free
In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G is
- a)k
- b)k + 1
- c)n - k - 1
- d)n - k
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a depth-first traversal of a graph G with n vertices, k edges are m...
Tree edges are the edges that are part of DFS tree. If there are x tree edges in a tree, then x+1 vertices in the tree. The output of DFS is a forest if the graph is disconnected. Let us see below simple example where graph is disconnected.
The above example matches with D option More Examples:
1) All vertices of Graph are connected. k must be n-1. We get number of connected components = n- k = n - (n-1) = 1
2) No vertex is connected. k must be 0. We get number of connected components = n- k = n - 0 = n
Most Upvoted Answer
In a depth-first traversal of a graph G with n vertices, k edges are m...
Explanation:
Depth-first Traversal in a Graph:
- In a depth-first traversal of a graph, we start from a source vertex and explore as far as possible along each branch before backtracking.
Tree Edges in Depth-first Traversal:
- In a depth-first traversal of a graph with n vertices, if k edges are marked as tree edges, this means that these edges are part of the spanning tree formed during the traversal.
Number of Connected Components:
- In a depth-first traversal, the number of connected components in the graph is equal to the number of times the traversal algorithm starts from a new vertex that has not been visited before.
Calculating Number of Connected Components:
- Initially, the graph has n vertices and is considered as one connected component.
- As the depth-first traversal progresses, each time a new unvisited vertex is encountered, a new connected component is formed.
- Since k edges are marked as tree edges, they form part of the spanning tree connecting vertices in the same connected component.
- Therefore, the number of connected components in the graph after the traversal is n - k.
Correct Answer:
- Hence, the correct answer is option 'd) n - k'.
Free Test
FREE
| Start Free Test |
Community Answer
In a depth-first traversal of a graph G with n vertices, k edges are m...
Tree edges are the edges that are part of DFS tree. If there are x tree edges in a tree, then x+1 vertices in the tree. The output of DFS is a forest if the graph is disconnected. Let us see below simple example where graph is disconnected.
The above example matches with D option More Examples:
1) All vertices of Graph are connected. k must be n-1. We get number of connected components = n- k = n - (n-1) = 1
2) No vertex is connected. k must be 0. We get number of connected components = n- k = n - 0 = n
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
In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. Can you explain this answer?
Question Description
In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. 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 In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. 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 In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. Can you explain this answer?.
In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. 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 In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. 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 In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. Can you explain this answer?.
Solutions for In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. 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 In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G isa)kb) k + 1c)n - k - 1d)n - kCorrect answer is option 'D'. 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