Practice Implication One (5.4.1) - Lecture - 54 - Discrete Mathematics

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9 questions

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6 sample questions

Question 1.
What does the term 'degree sequence' refer to in graph theory?
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Think about what degree means for a vertex.
Question 2.
True or False: A vertex can have a negative degree.
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Consider what a degree represents.
3Question 3.
What is the degree sequence of a graph?
- A list of the edges in ascending order
- The list of edge weights
- The list of vertices' degrees in non-increasing order
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Consider how you list the degrees.
4Question 4.
True or False: All sequences that contain non-negative integers can be graphic.
- True
- False
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Reflect on examples that couldn't satisfy graphical conditions.
Question 5.
Construct a graphic sequence of your own with five vertices and explain why it is graphic.
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Think about the connections you can make that meet the degree needs.
Question 6.
Apply the Havel-Hakimi theorem to the sequence (8, 6, 6, 4, 2, 1). Show all steps to verify its graphic nature.
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Follow the reduction process diligently and ensure you count correctly.

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