22.4.2. Using DFS for Cycle Detection

Try these first

1. 1.

   Define a cycle in a graph.

   Hint

   Think about returning to the same point without retracing edges.

2. 2.

   What does DFS stand for?

   Hint

   It's a common graph traversal algorithm.

3. 3.

   What is a cycle in graph theory?

   • A path that starts and ends at different vertices
   • A path that starts and ends at the same vertex
   • A connection between two vertices

   Hint

   Consider paths in a circle.

4. 4.

   Does a back edge in a directed graph always indicate a cycle?

   • True
   • False

   Hint

   What does a back edge connect to?

5. 5.

   You are given a directed graph. Explain why the presence of a back edge indicates a cycle. Provide an example.

   Hint

   Sketch the graph to visualize the back edge.

6. 6.

   Create a simple undirected graph and explain how you would use DFS to check for cycles.

   Hint

   Focus on marking visited nodes and avoiding the parent node.