5.2.3. Example Sequences

Try these first

1. 1.

   What is a degree sequence?

   Hint

   Think about how you order numbers in a list.

2. 2.

   Can a degree sequence have negative numbers?

   Hint

   Consider the nature of a vertex. Can it have a negative connection?

3. 3.

   What is a condition for a sequence to be graphic?

   • The sum of degrees must be odd
   • The sum of degrees must be even
   • All should be equal

   Hint

   Think about what happens to the edges.

4. 4.

   True or False: All sequences that start with zeros can never be graphic.

   • True
   • False

   Hint

   What would a zero degree imply?

5. 5.

   Given the sequence (3, 2, 2, 1), perform the Havel-Hakimi process and determine if it's graphic.

   Hint

   Follow each step carefully and keep the numbers aligned!

6. 6.

   Explain why the sequence (8, 6, 4, 4, 2) cannot be represented as a graphic sequence.

   Hint

   Check your arithmetic when summing those degrees!