5.4.2. Implication Two

Try these first

1. 1.

   What is a degree sequence?

   Hint

   Think of the vertex degrees.

2. 2.

   Can a degree sequence contain negative numbers?

   Hint

   Consider what a degree represents.

3. 3.

   What is a graphic sequence?

   • A sequence of positive integers only
   • A sequence that can represent a simple graph
   • Any sequence of numbers

   Hint

   Consider what conditions are required in graph theory.

4. 4.

   True or False: Every degree sequence must have at least one vertex with a degree of 0.

   • True
   • False

   Hint

   Think about full connectivity.

5. 5.

   Imagine a degree sequence of (4, 4, 4, 2). Determine if it is graphic and explain your reasoning thoroughly.

   Hint

   Try drawing it out!

6. 6.

   Construct two sequences, one graphic and one non-graphic, justify your choices.

   Hint

   Visualize graph connectivity!