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Which of following option is not correct regarding depth first searching?
  • a)
    In a depth-first traversal of a graph G with V vertices, E edges are marked as tree edges. The number of connected components in G is (E – V).
  • b)
    Depth-first search requires O(V2) time if implemented with an adjacency matrix.
  • c)
    Depth-first search requires O(V + E) time if implemented with adjacency lists
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Which of following option is not correct regarding depth first searchi...
In a depth-first traversal of a graph G with V vertices, E edges are marked as tree edges. The number of connected components in G is (V – E).
Only option (A) is false.
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Which of following option is not correct regarding depth first searchi...
Explanation:

Depth-First Traversal in Graphs:
- Depth-first traversal of a graph involves visiting each vertex and then recursively visiting all of its adjacent vertices.
- During this traversal, edges are classified as tree edges, back edges, forward edges, or cross edges.

Connected Components Calculation:
- In a depth-first traversal of a graph G with V vertices, E edges are marked as tree edges.
- The number of connected components in G can be calculated as (E - V).
- This is because in a connected graph, the number of edges is always one less than the number of vertices in the spanning tree.

Time Complexity of Depth-First Search:
- Depth-first search implemented with an adjacency matrix requires O(V^2) time.
- This is because for each vertex, we need to check all V vertices to determine adjacent vertices.
- Depth-first search implemented with adjacency lists requires O(V + E) time.
- This is because we need to visit each vertex once and each edge once in the adjacency list representation.

Conclusion:
- The statement in option 'A' that the number of connected components in G is (E - V) in a depth-first traversal is incorrect.
- The correct calculation for connected components in a graph G with V vertices and E edges is (E - V + C), where C is the number of connected components in the graph.
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Which of following option is not correct regarding depth first searching?a)In a depth-first traversal of a graph G with V vertices, E edges are marked as tree edges. The number of connected components in G is (E – V).b)Depth-first search requires O(V2) time if implemented with an adjacency matrix.c)Depth-first search requires O(V + E) time if implemented with adjacency listsd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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Which of following option is not correct regarding depth first searching?a)In a depth-first traversal of a graph G with V vertices, E edges are marked as tree edges. The number of connected components in G is (E – V).b)Depth-first search requires O(V2) time if implemented with an adjacency matrix.c)Depth-first search requires O(V + E) time if implemented with adjacency listsd)None of theseCorrect 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 Which of following option is not correct regarding depth first searching?a)In a depth-first traversal of a graph G with V vertices, E edges are marked as tree edges. The number of connected components in G is (E – V).b)Depth-first search requires O(V2) time if implemented with an adjacency matrix.c)Depth-first search requires O(V + E) time if implemented with adjacency listsd)None of theseCorrect 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 Which of following option is not correct regarding depth first searching?a)In a depth-first traversal of a graph G with V vertices, E edges are marked as tree edges. The number of connected components in G is (E – V).b)Depth-first search requires O(V2) time if implemented with an adjacency matrix.c)Depth-first search requires O(V + E) time if implemented with adjacency listsd)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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