5.3 - Characterization of Graphic Sequences
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Practice Questions
Test your understanding with targeted questions
What is the degree sequence of the graph with vertices of degrees 3, 2, and 1?
💡 Hint: List the degrees in non-increasing order.
Is the sequence (4, 3, 2, 1) a graphic sequence?
💡 Hint: Try to visualize a graph.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which of the following conditions must a sequence meet to be considered graphic?
💡 Hint: Recall the relationship between edges and vertex degrees.
True or False: Every non-negative sequence is a graphic sequence.
💡 Hint: Consider the necessary conditions we've discussed.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a sequence (6, 5, 4, 3, 2, 1), prove whether this is a graphic sequence using the Havel-Hakimi theorem.
💡 Hint: Calculate the sum to verify.
Construct a simple graph from the degree sequence (2, 2, 2, 2).
💡 Hint: Ensure each vertex connects with exactly two others.
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