4.5 - Question 4
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Practice Questions
Test your understanding with targeted questions
What is the vertex set of the Cartesian product if G1 has vertices {A, B} and G2 has vertices {1, 2}?
💡 Hint: Consider pairwise combinations of vertices.
Define the degree of vertex (A, 2) if vertex A in G1 has degree 2 and vertex 2 in G2 has degree 3.
💡 Hint: Add the degrees of A and vertex 2.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Cartesian product of two graphs produce?
💡 Hint: Think about how we structure new vertices from existing ones.
True or False: The edges of the Cartesian product are solely based on edges from the first graph.
💡 Hint: Remember the conditions for forming edges.
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Challenge Problems
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Given two graphs where G1 has 4 vertices and 2 edges, G2 has 3 vertices and 2 edges, find the Cartesian product of the two graphs including the vertex and edge counts.
💡 Hint: Apply the previous edge counting formulas carefully to both graphs.
Create a unique Cartesian product for G1 with a tree structure and G2 as a cycle graph. Discuss the resulting graph structure and edge counts.
💡 Hint: Explore specific characteristics of tree and cycle interactions.
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