5.4.1 - Implication One
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Practice Questions
Test your understanding with targeted questions
What does the term 'degree sequence' refer to in graph theory?
💡 Hint: Think about what degree means for a vertex.
True or False: A vertex can have a negative degree.
💡 Hint: Consider what a degree represents.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the degree sequence of a graph?
💡 Hint: Consider how you list the degrees.
True or False: All sequences that contain non-negative integers can be graphic.
💡 Hint: Reflect on examples that couldn't satisfy graphical conditions.
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Challenge Problems
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Construct a graphic sequence of your own with five vertices and explain why it is graphic.
💡 Hint: Think about the connections you can make that meet the degree needs.
Apply the Havel-Hakimi theorem to the sequence (8, 6, 6, 4, 2, 1). Show all steps to verify its graphic nature.
💡 Hint: Follow the reduction process diligently and ensure you count correctly.
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