24.1.5. Degree of a Vertex

Try these first

1. 1.

   What is the degree of vertex A if it connects to three edges?

   Hint

   Count each connecting edge.

2. 2.

   True or False: A self-loop adds one to the degree of a vertex.

   Hint

   Recall how we define self-loops.

3. 3.

   What is the degree of a vertex?

   • Number of edges connected to it
   • Number of paths to it
   • The weight of the vertex

   Hint

   Think about the count of edges incident to the vertex.

4. 4.

   True or False: The Handshaking Theorem concludes that the number of odd-degree vertices is even.

   • True
   • False

   Hint

   Recall the theorem and its implications.

5. 5.

   Given a graph with 7 vertices and 10 edges, what can you infer about the total degree and the number of odd-degree vertices?

   Hint

   Use the Handshaking theorem to deduce the conclusion.

6. 6.

   Create an undirected graph with 3 odd-degree vertices and explain why this is not possible.

   Hint

   Consider how odd numbers add together.