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Consider the following statements:
S1 : DFS of a directed graph always produces the same number of edges in the traversal, irrespective of the starting vertex.
S2 : If all of the back edges that are found while DFS traversal on directed graph are removed, the resulting graph is acyclic.
Q. Which of the following statements above are valid?
S2 : If all of the back edges that are found while DFS traversal on directed graph are removed, the resulting graph is acyclic.
Q. Which of the following statements above are valid?
- a)Both S1 and S2 are valid
- b)Only S1 is valid
- c)Only S2 is valid
- d)Neither s1 nor S2 is valid
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the following statements:S1 :DFS of a directed graph always p...
Statement S1 : consider the graph
Starting with A (source vertex ) we will get 2 edges Starting with B will get only 1 edge Starting with C we will get no edge Therefore DFS on directed graph may not give same number of edges. Statement S2 : Back edges are those edges (u,v) connecting a vertex u to an ancestor u in a depth-first tree. Self-loops are considered to be back edges. Back edges describe descendant-to-ancestor relations, as they lead from “high” to “low” nodes. Suppose that there is a back edge (u, v). Then vertex v is an ancestor of vertex u in the depth-first forest. There is thus a path from v to u in G, and the back edge (u,v) completes a cycle. Removing the back edge will break the cycle. Therefore removing all the back edges will make the graph acyclic. So the statement is true.
Most Upvoted Answer
Consider the following statements:S1 :DFS of a directed graph always p...
Statement S1: DFS of a directed graph always produces the same number of edges in the traversal, irrespective of the starting vertex.
DFS (Depth First Search) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It can be used to traverse both directed and undirected graphs.
The statement claims that regardless of the starting vertex, the number of edges traversed in a DFS of a directed graph will always be the same. However, this statement is false.
Counterexample:
Consider a directed graph with two vertices, A and B, and a single edge from A to B. If we perform a DFS starting from vertex A, we will traverse the edge from A to B. However, if we start the DFS from vertex B, there are no outgoing edges from B, so the traversal will not have any edges. Therefore, the number of edges traversed in the DFS depends on the starting vertex, and statement S1 is invalid.
Statement S2: If all of the back edges that are found while DFS traversal on a directed graph are removed, the resulting graph is acyclic.
A back edge is an edge that connects a vertex to one of its ancestors in the DFS traversal. In a directed graph, if a back edge exists, it indicates the presence of a cycle.
The statement claims that if all the back edges found during a DFS traversal are removed, the resulting graph will be acyclic. This statement is true.
Explanation:
When a back edge is removed, it breaks the cycle in the graph. This is because the back edge connects a vertex to one of its ancestors, which means there is a path that leads back to the same vertex. By removing this edge, the path is no longer valid, and the cycle is eliminated.
Removing all the back edges in a DFS traversal will eventually remove all cycles from the graph, resulting in an acyclic graph. Therefore, statement S2 is valid.
In conclusion, only statement S2 is valid. The DFS of a directed graph does not always produce the same number of edges, but if all the back edges are removed, the resulting graph becomes acyclic.
DFS (Depth First Search) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It can be used to traverse both directed and undirected graphs.
The statement claims that regardless of the starting vertex, the number of edges traversed in a DFS of a directed graph will always be the same. However, this statement is false.
Counterexample:
Consider a directed graph with two vertices, A and B, and a single edge from A to B. If we perform a DFS starting from vertex A, we will traverse the edge from A to B. However, if we start the DFS from vertex B, there are no outgoing edges from B, so the traversal will not have any edges. Therefore, the number of edges traversed in the DFS depends on the starting vertex, and statement S1 is invalid.
Statement S2: If all of the back edges that are found while DFS traversal on a directed graph are removed, the resulting graph is acyclic.
A back edge is an edge that connects a vertex to one of its ancestors in the DFS traversal. In a directed graph, if a back edge exists, it indicates the presence of a cycle.
The statement claims that if all the back edges found during a DFS traversal are removed, the resulting graph will be acyclic. This statement is true.
Explanation:
When a back edge is removed, it breaks the cycle in the graph. This is because the back edge connects a vertex to one of its ancestors, which means there is a path that leads back to the same vertex. By removing this edge, the path is no longer valid, and the cycle is eliminated.
Removing all the back edges in a DFS traversal will eventually remove all cycles from the graph, resulting in an acyclic graph. Therefore, statement S2 is valid.
In conclusion, only statement S2 is valid. The DFS of a directed graph does not always produce the same number of edges, but if all the back edges are removed, the resulting graph becomes acyclic.
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Consider the following statements:S1 :DFS of a directed graph always produces the same number of edges in the traversal, irrespective of the starting vertex.S2 :If all of the back edges that are found while DFS traversal on directed graph are removed, the resulting graph is acyclic.Q. Which of the following statements above are valid?a)Both S1 and S2 are validb)Only S1 is validc)Only S2 is validd)Neither s1 nor S2 is validCorrect answer is option 'C'. Can you explain this answer?
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Consider the following statements:S1 :DFS of a directed graph always produces the same number of edges in the traversal, irrespective of the starting vertex.S2 :If all of the back edges that are found while DFS traversal on directed graph are removed, the resulting graph is acyclic.Q. Which of the following statements above are valid?a)Both S1 and S2 are validb)Only S1 is validc)Only S2 is validd)Neither s1 nor S2 is validCorrect answer is option 'C'. 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 Consider the following statements:S1 :DFS of a directed graph always produces the same number of edges in the traversal, irrespective of the starting vertex.S2 :If all of the back edges that are found while DFS traversal on directed graph are removed, the resulting graph is acyclic.Q. Which of the following statements above are valid?a)Both S1 and S2 are validb)Only S1 is validc)Only S2 is validd)Neither s1 nor S2 is validCorrect answer is option 'C'. 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 Consider the following statements:S1 :DFS of a directed graph always produces the same number of edges in the traversal, irrespective of the starting vertex.S2 :If all of the back edges that are found while DFS traversal on directed graph are removed, the resulting graph is acyclic.Q. Which of the following statements above are valid?a)Both S1 and S2 are validb)Only S1 is validc)Only S2 is validd)Neither s1 nor S2 is validCorrect answer is option 'C'. Can you explain this answer?.
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