4.1.3. Lecture - 53

Try these first

1. 1.

   What is vertex connectivity?

   Hint

   Think about removing points to create isolation.

2. 2.

   Define edge connectivity.

   Hint

   Consider how many connections you need to sever.

3. 3.

   What must be true about vertex connectivity compared to edge connectivity?

   • Vertex connectivity is greater
   • Vertex connectivity is less
   • Vertex connectivity is equal

   Hint

   Review the properties discussed about connectivity.

4. 4.

   True or False: The minimum degree of a graph is always less than or equal to its vertex connectivity.

   • True
   • False

   Hint

   Consider the definitions of degree and connectivity.

5. 5.

   Prove that for a simple graph with vertex connectivity l and edge connectivity m, if l > m, the graph must contain at least one cut vertex.

   Hint

   Use contradiction by assuming a scenario where no cut vertices exist.

6. 6.

   Construct a non-complete graph that meets the criteria: vertex connectivity = edge connectivity = 3, and state why it is not complete.

   Hint

   Consider structures like cycles or trees that meet the conditions.