22.6.1. Articulation Points

Try these first

1. 1.

   Define an articulation point.

   Hint

   Think about vertices that act as bridges in graphs.

2. 2.

   What does DFS stand for?

   Hint

   How do you explore deeply into a graph?

3. 3.

   What is an articulation point?

   • A vertex that connects two graphs
   • A vertex that can be removed without affecting connectivity
   • A vertex whose removal increases connected components

   Hint

   Think about vertices that serve as important connectors.

4. 4.

   True or False: Removing any vertex will always lead to an increase in the number of components.

   • True
   • False

   Hint

   Consider what happens to a graph when you remove different types of vertices.

5. 5.

   Given a graph, analyze it using DFS to identify all articulation points. Describe your thought process and the steps you take.

   Hint

   Remember how discovery times help identify critical connections.

6. 6.

   Design a scenario where removing an articulation point would disrupt a network severely. Explain the ramifications.

   Hint

   Think about how crucial connections operate in complex systems.