24.1.8.3. Wheel Graph

Try these first

1. 1.

   What is a wheel graph?

   Hint

   Think about the circular structure with a central point.

2. 2.

   How many edges does W_3 have?

   Hint

   Count the edges connecting the central vertex to each of the cycle vertices.

3. 3.

   What defines a wheel graph?

   • A graph with no edges.
   • A graph connecting every vertex to another.
   • A graph with a central vertex connected to a cycle.

   Hint

   Imagine the structure of a wheel with spokes.

4. 4.

   True or False: A wheel graph cannot have cycles.

   • True
   • False

   Hint

   Consider what makes a wheel graph.

5. 5.

   Discuss the implications of adding more nodes to the cycle in a wheel graph and how it alters connectivity.

   Hint

   Think about how many connections each node gains.

6. 6.

   Construct W_6 and analyze the number of edges and vertices. Discuss the structural changes.

   Hint

   Count the spokes connecting the center.