4.1.1. Prof. Ashish Choudhury

Try these first

1. 1.

   Define vertex connectivity in your own words.

   Hint

   Think about how to separate the graph into smaller parts.

2. 2.

   What two factors define edge connectivity?

   Hint

   Consider how removing edges impacts the connections.

3. 3.

   What is vertex connectivity?

   • The minimum edges to remove
   • The minimum vertices to disconnect
   • The count of nodes

   Hint

   Recall our definitions from class.

4. 4.

   True or False: Edge connectivity can be less than vertex connectivity.

   • True
   • False

   Hint

   Think about how edges and vertices relate.

5. 5.

   Construct a graph given l = 2, m = 3, and n = 5. Verify its connectivity.

   Hint

   Use copies of complete graphs to maintain degree and connectivity.

6. 6.

   Given two graphs, G1 with 4 edges and G2 with 6, find how many edges the Cartesian product of G1 and G2 will yield.

   Hint

   Review how pairs correspond to edges in both original graphs.