4.7. Combinatorial Proof

Try these first

1. 1.

   Define vertex connectivity in your own words.

   Hint

   What is the defining factor for disconnection?

2. 2.

   What is edge connectivity?

   Hint

   Consider how edges affect graph stability.

3. 3.

   What is the minimum degree necessary to achieve vertex connectivity of 3?

   • 1
   • 2
   • 3
   • 4

   Hint

   Consider how many connections are required.

4. 4.

   True or False: Removing one edge can always increase vertex connectivity.

   • True
   • False

   Hint

   Evaluate if edge removal affects disconnection.

5. 5.

   Given a graph with 5 vertices and specific connections, determine the vertex and edge connectivity.

   Hint

   Consider removal strategies for both vertices and edges.

6. 6.

   Create a combinatorial proof showing the relationship between the number of edges in a complete graph and its constructive components.

   Hint

   Examine edge counts from multiple perspectives.