Which of the following statements is true regarding DFS and cycles in directed graphs?2 pointsDFS can detect cycles only in undirected graphs, not in directed graphsDFS can detect cycles in directed graphs by keeping track of visited verticesDFS cannot detect cycles in directed graphs; it requires a separate algorithmDFS can only detect cycles in directed graphs if they are Hamiltonian cycles
Question
Which of the following statements is true regarding DFS and cycles in directed graphs?2 pointsDFS can detect cycles only in undirected graphs, not in directed graphsDFS can detect cycles in directed graphs by keeping track of visited verticesDFS cannot detect cycles in directed graphs; it requires a separate algorithmDFS can only detect cycles in directed graphs if they are Hamiltonian cycles
Solution
The true statement regarding DFS (Depth-First Search) and cycles in directed graphs is: "DFS can detect cycles in directed graphs by keeping track of visited vertices".
Here's why:
DFS is a graph traversal algorithm that can be used to search for cycles in both directed and undirected graphs. The key to detecting cycles is to keep track of the vertices that have been visited during the traversal.
In the context of DFS, a cycle is detected in a directed graph when a vertex is encountered that is already in the recursion stack. If we reach a vertex that is already in the recursion stack, then there is a cycle in the tree.
The other statements are incorrect because DFS can indeed detect cycles in directed graphs, it doesn't require a separate algorithm to do so, and it doesn't only detect cycles if they are Hamiltonian cycles.
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