5.2.1. Definition

Try these first

1. 1.

   What is a degree of a vertex?

   Hint

   Think about how many lines connect to a point in a graph.

2. 2.

   Define a graphic sequence.

   Hint

   Remember it must fulfill certain criteria.

3. 3.

   What defines a degree sequence?

   • The total edges
   • List of vertex degrees
   • Sum of the degrees

   Hint

   Think about what this sequence pertains to.

4. 4.

   True or False: A graphic sequence can have a sum of degrees that is odd.

   • True
   • False

   Hint

   Consider how edges relate to vertex degrees.

5. 5.

   Evaluate the sequence (8, 3, 2, 2, 0, 1). Is it graphic? Apply any method you can think of.

   Hint

   Consider the maximum degree and neighboring requirements.

6. 6.

   Apply the Havel-Hakimi theorem to the sequence (4, 2, 2, 2). Explain each step.

   Hint

   Visualize how edges may need to be formed during reductions.