1.1. Lecture - 54

Try these first

1. 1.

   List the requirements for a sequence to be considered graphic.

   Hint

   Recall the acronym NEE.

2. 2.

   Are the vertex degrees in a graphic sequence required to be distinct?

   Hint

   Think about examples that can have identical values.

3. 3.

   What is one requirement for a sequence to be graphic?

   • They can have negative values.
   • Sum must be odd.
   • Non-negative values.

   Hint

   Think about physical graph representation.

4. 4.

   True or False: The sequence (5,3,1) is graphic.

   • True
   • False

   Hint

   Check the connectivity of the vertex with the highest degree.

5. 5.

   Show that the sequence (5, 4, 3, 3, 2, 1) can be graphic, and construct a corresponding graph.

   Hint

   Use the Havel-Hakimi theorem to simplify your process.

6. 6.

   Using the Havel-Hakimi theorem, prove whether (6, 5, 4, 3, 3) is graphic.

   Hint

   Always rearrange after each step to maintain order.