24.1.4. Terminologies related to Undirected Graphs

Try these first

1. 1.

   Define a vertex in the context of a graph.

   Hint

   Think of it as the 'dots' on a diagram.

2. 2.

   What does it mean for two vertices to be adjacent?

   Hint

   Look for direct connections.

3. 3.

   What defines a complete graph?

   • A graph with no edges.
   • A graph where each pair of vertices is connected.
   • A graph with only even degree vertices.

   Hint

   Think about connections between nodes.

4. 4.

   True or False: An undirected graph can have an odd number of vertices of odd degree.

   • True
   • False

   Hint

   Consider how edges contribute to vertex degrees.

5. 5.

   Create a bipartite graph with 6 vertices, where 3 belong to one set and 3 to another. Ensure all vertices are connected.

   Hint

   Visualize how each group can only connect to the other group.

6. 6.

   Demonstrate the handshaking theorem with a graph of your choice. Provide the degree of each vertex and verify the theorem.

   Hint

   List out the edges and their contributions to each vertex.