Practice Question 9: Proving A Graphic Sequence (6) - Question 9: Proving a Graphic Sequence

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8 questions

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6 sample questions

Question 1.
Define a graphic sequence.
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Think about what a graph represents.
Question 2.
What does the Havel-Hakimi theorem help prove?
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Consider what path or edges we can visualize.
3Question 3.
Is the sequence [5, 2, 2, 1] graphic?
- True
- False
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Check the degrees against how many connections they can create.
4Question 4.
What condition must be met for a sequence to be graphic?
- All integers must be even
- Sum of degrees must be even
- Degree values must be prime
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Think of how edges are counted in a graph.
Question 5.
Prove that the sequence [6, 5, 4, 4, 3, 2] is graphic by constructing a graph.
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Remember to adjust your connections based on degree constraints.
Question 6.
Using the Havel-Hakimi method, show that the sequence [1, 1, 1, 0] cannot be graphic.
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Focus on the odd count of degrees in the sequence.

4 more questions in this section. Enroll free to practise them all.