Practice Characterization Of Graphic Sequences (5.3) - Lecture - 54 - Discrete Mathematics

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6 sample questions

Question 1.
What is the degree sequence of the graph with vertices of degrees 3, 2, and 1?
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List the degrees in non-increasing order.
Question 2.
Is the sequence (4, 3, 2, 1) a graphic sequence?
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Try to visualize a graph.
3Question 3.
Which of the following conditions must a sequence meet to be considered graphic?
- All degrees must be negative.
- The sum of degrees must be even.
- The sequence must be in random order.
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Recall the relationship between edges and vertex degrees.
4Question 4.
True or False: Every non-negative sequence is a graphic sequence.
- True
- False
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Consider the necessary conditions we've discussed.
Question 5.
Given a sequence (6, 5, 4, 3, 2, 1), prove whether this is a graphic sequence using the Havel-Hakimi theorem.
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Calculate the sum to verify.
Question 6.
Construct a simple graph from the degree sequence (2, 2, 2, 2).
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Ensure each vertex connects with exactly two others.

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