Which of the following traversal methods is typically used to detect cycles in an undirected graph?Depth-First Search (DFS)Breadth-First Search (BFS)Dijkstra's algorithmPrim's algorithm

The traversal method typically used to detect cycles in an undirected graph is Depth-First Search (DFS).

Here's a step-by-step explanation:

1. Start at any vertex in the graph.
2. Use DFS to explore the graph. In DFS, you start at a given vertex and explore as far as possible along each branch before backtracking.
3. While traversing, keep track of the vertices you've visited and the vertex you came from.
4. If you encounter a vertex that has already been visited and it is not the vertex you came from, then there is a cycle in the graph.

Breadth-First Search (BFS), Dijkstra's algorithm, and Prim's algorithm are not typically used to detect cycles in an undirected graph. BFS is used for shortest path and flood fill problems, Dijkstra's algorithm is used for finding the shortest paths from a single node to all other nodes in a weighted graph, and Prim's algorithm is used for finding a minimum spanning tree in a weighted undirected graph.

The traversal method typically used to detect cycles in an undirected graph is Depth-First Search (DFS).

Here's a step-by-step explanation:

1. Start at any vertex in the graph.
2. Use DFS to explore the graph. In DFS, you start at a root node, then explore as far as possible along each branch before backtracking.
3. While traversing, keep track of the vertices you've visited and the parent of each vertex.
4. If you encounter a vertex that has already been visited and it is not the parent of the current vertex, then there is a cycle in the graph.

This is because in an undirected graph, the only way you can revisit a vertex from a different vertex is if there is a cycle.