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...
Understanding Depth-First Traversal
In a depth-first traversal of a graph \( G \), we explore as far as possible along each branch before backtracking. During this traversal, edges that lead to new vertices are classified as tree edges.
Key Components of the Graph
- Vertices (\( n \)): The total number of nodes in the graph.
- Edges (\( k \)): The number of edges that are considered tree edges during the traversal.
- Connected Components: A connected component is a subset of the graph where there is a path between any two vertices in that subset.
Relation Between Edges and Components
When we conduct a depth-first search (DFS):
- Each time we discover a new connected component, we start a new tree from an unvisited vertex.
- For each component, the number of edges \( k \) connects \( n - c \) vertices, where \( c \) is the number of components.
Formula Derivation
1. Tree Edges: The \( k \) tree edges connect \( k + 1 \) vertices (since \( k \) edges connect \( k + 1 \) nodes in a tree structure).
2. Connected Components: The number of connected components \( C \) can be derived from the formula:
\[
C = n - k
\]
Here, \( n \) is the total vertices, and \( k \) is the number of edges in the spanning tree.
3. Conclusion: Therefore, the number of connected components is given by:
\[
\text{Number of Components} = n - k
\]
Final Answer
Thus, the number of connected components in graph \( G \) is \( n - k \), confirming that option 'D' is correct.
In a depth-first traversal of a graph \( G \), we explore as far as possible along each branch before backtracking. During this traversal, edges that lead to new vertices are classified as tree edges.
Key Components of the Graph
- Vertices (\( n \)): The total number of nodes in the graph.
- Edges (\( k \)): The number of edges that are considered tree edges during the traversal.
- Connected Components: A connected component is a subset of the graph where there is a path between any two vertices in that subset.
Relation Between Edges and Components
When we conduct a depth-first search (DFS):
- Each time we discover a new connected component, we start a new tree from an unvisited vertex.
- For each component, the number of edges \( k \) connects \( n - c \) vertices, where \( c \) is the number of components.
Formula Derivation
1. Tree Edges: The \( k \) tree edges connect \( k + 1 \) vertices (since \( k \) edges connect \( k + 1 \) nodes in a tree structure).
2. Connected Components: The number of connected components \( C \) can be derived from the formula:
\[
C = n - k
\]
Here, \( n \) is the total vertices, and \( k \) is the number of edges in the spanning tree.
3. Conclusion: Therefore, the number of connected components is given by:
\[
\text{Number of Components} = n - k
\]
Final Answer
Thus, the number of connected components in graph \( G \) is \( n - k \), confirming that option 'D' is correct.
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
|
|
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