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3 cards from this section. Quick, good the night before a test.
What is a degree sequence?
Think about how you count edges connected to vertices.
Is the sequence (5, 3, 1, 0) a graphic sequence?
Remember the sum of degrees must be even.
What is the first step in applying the Havel-Hakimi theorem?
What do we do with the first value?
True or False: The sum of the degrees in any graphic sequence must be odd.
Think about the properties of edges and vertices.
Formulate a degree sequence of your choice and prove using the Havel-Hakimi theorem whether it’s graphic or not.
Apply each step and track the degrees closely.
Construct a graph based on a successful realization of a graphic sequence. Demonstrate it visually.
Drawing it helps visualize the relationships that confirm the degrees.
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