5.4.2.2. Case 2: Vertex v is Not Adjacent

Try these first

1. 1.

   Determine if the sequence (3, 2, 2) is graphic.

   Hint

   Check if the sum is even.

2. 2.

   Is the sequence (0, 0, 0) graphic?

   Hint

   Consider the nature of disconnected vertices.

3. 3.

   What must the sum of a graphic sequence be?

   • Odd
   • Even
   • Prime

   Hint

   Consider how edges are counted in a graph.

4. 4.

   The Havel-Hakimi theorem is used to verify if a sequence is graphic. True or False?

   • True
   • False

   Hint

   Think of the iterative method employed.

5. 5.

   Given the sequence (8, 5, 5, 4, 4, 3, 2), assess if it's graphic and explain your reasoning.

   Hint

   Use the Havel-Hakimi method step by step.

6. 6.

   Analyze the sequence (10, 3, 3, 2, 1) and determine if it can exist as a graphic sequence.

   Hint

   Look for contradictions when applying the theorem.