6 - Question 9: Proving a Graphic Sequence
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Practice Questions
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Define a graphic sequence.
💡 Hint: Think about what a graph represents.
What does the Havel-Hakimi theorem help prove?
💡 Hint: Consider what path or edges we can visualize.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Is the sequence [5, 2, 2, 1] graphic?
💡 Hint: Check the degrees against how many connections they can create.
What condition must be met for a sequence to be graphic?
💡 Hint: Think of how edges are counted in a graph.
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Challenge Problems
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Prove that the sequence [6, 5, 4, 4, 3, 2] is graphic by constructing a graph.
💡 Hint: Remember to adjust your connections based on degree constraints.
Using the Havel-Hakimi method, show that the sequence [1, 1, 1, 0] cannot be graphic.
💡 Hint: Focus on the odd count of degrees in the sequence.
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