Practice Question 4 - 4.5 | 4. Prof. Ashish Choudhury | Discrete Mathematics - Vol 3
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4.5 - Question 4

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

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.

Question 2

Easy

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

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does the Cartesian product of two graphs produce?

  • A single graph with no edges
  • Ordered pairs of vertices
  • Two separate vertex sets

💡 Hint: Think about how we structure new vertices from existing ones.

Question 2

True or False: The edges of the Cartesian product are solely based on edges from the first graph.

  • True
  • False

💡 Hint: Remember the conditions for forming edges.

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Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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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