24.1.6. Handshaking Theorem

Try these first

1. 1.

   What is the degree of a vertex connected to 4 edges?

   Hint

   The degree is simply the count of edges.

2. 2.

   Can an undirected graph have an empty edge set? Why?

   Hint

   Focus on the definition of a graph.

3. 3.

   What does the Handshaking Theorem state?

   Hint

   Consider how vertices are related through edges.

4. 4.

   Does a self-loop contribute one or two to a vertex's degree?

   • True
   • False

   Hint

   Recall the definition of degree.

5. 5.

   Create a graph with 5 vertices where the degrees of vertices are 4, 3, 3, 2, and 1. Ensure the graph is undirected. Is there any violation of the Handshaking Theorem?

   Hint

   Check the Handshaking Theorem for validation.

6. 6.

   In a connected graph, if every vertex has an even degree, show how you can form an Eulerian circuit.

   Hint

   Reflect on Euler's properties.