24.1.8. Special Types of Undirected Graphs

Try these first

1. 1.

   Define a complete graph.

   Hint

   Think about how vertices relate to one another.

2. 2.

   What is the minimum number of vertices in a cycle graph?

   Hint

   Consider how many distinct points form a closed shape.

3. 3.

   What is a complete graph?

   • A graph with no edges
   • A graph where every pair of distinct vertices is connected
   • A graph with only one vertex

   Hint

   Visualize how every vertex interacts.

4. 4.

   Which of the following is an example of a cycle graph?

   • A line graph
   • A graph forming a closed loop
   • A disconnected graph

   Hint

   Think of shapes that enclose area.

5. 5.

   Construct and illustrate a bipartite graph with 4 vertices in one set and 3 in another, ensuring all connections are proper according to bipartite rules.

   Hint

   Make sure to depict no edges connecting the same set.

6. 6.

   Explain the significance of the handshaking theorem in relation to even and odd degree vertices in bipartite graphs.

   Hint

   Think about how edges link vertices on different sides.