4.4.1. Connected Non-Complete Graph

Try these first

1. 1.

   What is vertex connectivity in a graph?

   Hint

   Think about how many vertices you would remove to break the connections.

2. 2.

   Define edge connectivity.

   Hint

   Consider how removing edges affects the connectivity.

3. 3.

   What is the relationship between vertex connectivity and edge connectivity?

   • Vertex connectivity is greater
   • Edge connectivity is greater
   • They are equal or vertex connectivity is less

   Hint

   Review the definitions of both terms.

4. 4.

   True or False: Every non-complete graph has a vertex connectivity greater than 0.

   • True
   • False

   Hint

   Think about what defines a non-complete graph.

5. 5.

   Construct a graph that demonstrates vertex connectivity of 4, edge connectivity of 5, and minimum degree of 6.

   Hint

   Think about density and how connections are made.

6. 6.

   Identify and explain a real-world scenario where maintaining vertex and edge connectivity is essential for communication networks.

   Hint

   Consider how removing connections affects data flow.