4.1.2. International Institute of Information Technology - Bangalore

Try these first

1. 1.

   What is vertex connectivity?

   Hint

   Think about how many nodes you could take out to break a path.

2. 2.

   If a graph has n vertices, what is the maximum number of edges it can have?

   Hint

   This counts every connection.

3. 3.

   What defines vertex connectivity?

   • The number of edges
   • Minimum vertex removal for disconnection
   • Minimum edges to maintain connection

   Hint

   Think about how you'd keep a group connected.

4. 4.

   True or False: Every complete graph has vertex connectivity equal to n-1.

   • True
   • False

   Hint

   Consider how many edges are possible in a complete structure.

5. 5.

   Construct two graphs where vertex and edge connectivity varies but both achieve the same minimum degree. Explain how it's achieved.

   Hint

   Use different configurations to maintain degree but vary edges.

6. 6.

   Design a simple graph with 6 vertices, ensuring that vertex connectivity is 4, while edge connectivity is lesser. Show configurations.

   Hint

   Think about groups that rely on fewer vertices while maintaining edge diversity.