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

Practice: Question 4

Lesson 4.5Prof. Ashish Choudhury

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9 questions

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6 sample questions

Question 1.
What is the vertex set of the Cartesian product if G1 has vertices {A, B} and G2 has vertices {1, 2}?
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Consider pairwise combinations of vertices.
Question 2.
Define the degree of vertex (A, 2) if vertex A in G1 has degree 2 and vertex 2 in G2 has degree 3.
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Add the degrees of A and vertex 2.
3Question 3.
What does the Cartesian product of two graphs produce?
- A single graph with no edges
- Ordered pairs of vertices
- Two separate vertex sets
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Think about how we structure new vertices from existing ones.
4Question 4.
True or False: The edges of the Cartesian product are solely based on edges from the first graph.
- True
- False
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Remember the conditions for forming edges.
Question 5.
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.
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Apply the previous edge counting formulas carefully to both graphs.
Question 6.
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.
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Explore specific characteristics of tree and cycle interactions.

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