5.1.2. Tutorial 9: Part II

Try these first

1. 1.

   What is a degree sequence?

   Hint

   Consider the connections each vertex has.

2. 2.

   Can a sequence containing a negative degree be considered graphic?

   Hint

   Think about the practical meaning of degrees.

3. 3.

   What condition must be met for a degree sequence to be graphic?

   • The sum must be odd
   • All values must be non-negative
   • It is isolated

   Hint

   Think about the physical meaning of a vertex's connections.

4. 4.

   Is the sequence [1, 2, 3] graphic?

   • True
   • False

   Hint

   Try sketching the connections.

5. 5.

   Given the sequence [6, 5, 4, 4, 3, 2], analyze whether it is graphic using the Havel-Hakimi theorem.

   Hint

   Follow the steps carefully and visualize the adjustments in graph degrees.

6. 6.

   Prove that the sequence [1, 1, 1, 1] is graphic. Provide a diagram or written explanation to support your answer.

   Hint

   Visuals help! Try sketching the connections between vertices.