5.2. Degree Sequence of a Graph

Try these first

1. 1.

   What is the degree of a vertex?

   Hint

   Think of how many friends a person has in a social network.

2. 2.

   Does a vertex degree can be negative?

   Hint

   Try to visualize it with real-life objects.

3. 3.

   What does the degree of a vertex represent?

   Hint

   Visualize how many paths lead to this vertex.

4. 4.

   True or False: The sum of degrees in any graph must be odd.

   • True
   • False

   Hint

   Remember how edges link two vertices.

5. 5.

   Evaluate whether the sequence [7, 6, 5, 4, 3, 2, 1] can be a degree sequence. Justify your answer using the Havel-Hakimi theorem.

   Hint

   Break down the highest number first!

6. 6.

   Design a simple graph for the degree sequence [3, 3, 3, 3] and outline the possible arrangements.

   Hint

   Consider how each vertex connects with others.