4.5.2 - Degree of Vertices in Cartesian Product
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Practice Questions
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Define the Cartesian product of two graphs.
💡 Hint: Think about ordered pairs and pairs of vertices.
What is the degree of a vertex?
💡 Hint: Count the connections!
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the degree of vertex (u,v) in the Cartesian product?
💡 Hint: Think about how the degrees interact together.
If a graph G has no edges, what is the degree of all vertices?
💡 Hint: Remember degrees count edges!
1 more question available
Challenge Problems
Push your limits with advanced challenges
Consider two graphs A and B where A has 3 vertices with degrees [0, 1, 2] and B has 3 vertices with degrees [1, 1, 1]. Calculate the degrees in the Cartesian Product.
💡 Hint: Assess every pair in the product using the summed degrees.
Given two graphs C and D, where C has a vertex of degree 4 and D with a vertex of degree 0, discuss the implications on the product graph's connectivity.
💡 Hint: Consider how degree zero affects the overall performance in connectivity.
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