4.2. Question 1

Try these first

1. 1.

   Define vertex connectivity.

   Hint

   Think about how many vertices can be removed.

2. 2.

   What does edge connectivity refer to?

   Hint

   Focus on the word 'edge' in the definition.

3. 3.

   What is the relationship between vertex and edge connectivity?

   • Vertex connectivity is greater than edge connectivity.
   • Vertex connectivity is less than or equal to edge connectivity.
   • They are the same.

   Hint

   Think about what you need to remove to disconnect the graph.

4. 4.

   True or False: Removing all edges will also remove vertex connectivity.

   • True
   • False

   Hint

   Consider how edges and vertices interact.

5. 5.

   How can you create a simple graph satisfying l = 2, m = 3, and n = 4? Discuss the necessary steps and properties.

   Hint

   Start with basic complete graphs and build from there.

6. 6.

   Discuss the impact on vertex connectivity if vertex degree decreases. How might this affect edge connectivity?

   Hint

   Think of connectivity as a chain reaction.