1.9. Cut Vertex and Cut Edge

Try these first

1. 1.

   Define a cut vertex.

   Hint

   Think about its role in connectivity.

2. 2.

   What happens to a graph when a cut edge is removed?

   Hint

   Consider the impact of cutting connections.

3. 3.

   What is a cut vertex?

   • An edge whose removal disconnects the graph.
   • A vertex whose removal disconnects the graph.
   • A type of graph.

   Hint

   Think about the role of vertices in maintaining graph structure.

4. 4.

   True or False: A cut edge increases the connectivity of a graph.

   • True
   • False

   Hint

   What happens when we remove a critical edge?

5. 5.

   Design a custom graph with at least three cut vertices and discuss the implications of their removal.

   Hint

   Use simple shapes and connections to create your graph.

6. 6.

   Analyze a subway system modeled as a graph. Identify the cut edges and discuss how their removal would affect travel.

   Hint

   Think about the importance of each subway line in connecting major areas.