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Is following statement true/false? A DFS of a directed graph always produces the same number of tree edges, i.e., independent of the order in which vertices are considered for DFS.
- a)True
- b)False
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Is following statement true/false? A DFS of a directed graph always pr...
Consider the following graph. If we start from 'a', then there is one tree edge. If we start from 'b', then there is no tree edge. a---->b
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Is following statement true/false? A DFS of a directed graph always pr...
False
Explanation:
A Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It uses a stack data structure to keep track of the vertices to visit.
In a DFS, the number of tree edges depends on the order in which the vertices are considered. The order of traversal determines the number and direction of the edges in the resulting DFS tree.
Example:
Consider the following directed graph:
A
/ \
B C
/ \ \
D E F
If we start the DFS at vertex A, the traversal order would be A -> B -> D -> E -> C -> F. In this case, there are 5 tree edges: (A, B), (B, D), (B, E), (A, C), (C, F).
However, if we start the DFS at vertex C, the traversal order would be C -> F -> A -> B -> D -> E. In this case, there are 4 tree edges: (C, F), (F, A), (A, B), (B, D).
As we can see, the number of tree edges in the DFS tree depends on the starting vertex and the order in which the vertices are considered. Therefore, the statement "A DFS of a directed graph always produces the same number of tree edges, i.e., independent of the order in which vertices are considered for DFS" is false.
Explanation:
A Depth-First Search (DFS) is a graph traversal algorithm that explores as far as possible along each branch before backtracking. It uses a stack data structure to keep track of the vertices to visit.
In a DFS, the number of tree edges depends on the order in which the vertices are considered. The order of traversal determines the number and direction of the edges in the resulting DFS tree.
Example:
Consider the following directed graph:
A
/ \
B C
/ \ \
D E F
If we start the DFS at vertex A, the traversal order would be A -> B -> D -> E -> C -> F. In this case, there are 5 tree edges: (A, B), (B, D), (B, E), (A, C), (C, F).
However, if we start the DFS at vertex C, the traversal order would be C -> F -> A -> B -> D -> E. In this case, there are 4 tree edges: (C, F), (F, A), (A, B), (B, D).
As we can see, the number of tree edges in the DFS tree depends on the starting vertex and the order in which the vertices are considered. Therefore, the statement "A DFS of a directed graph always produces the same number of tree edges, i.e., independent of the order in which vertices are considered for DFS" is false.
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