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Question 4 Let C; be a simple cycle of length 5 on the vertex set {1,2, 3, 4, 5} and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graph on vertex set {1,2,3, 4, 5, a, b, c, d} where the edges between numbered vertices come from C3, the edges between lettered vertices come from K4 and we take all possible edges of the form xy where x is a number and y is a letter. Answer the following questions.

Question 4 Let C; be a simple cycle of length 5 on the vertex set {1,2, 3, 4, 5} and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graph on vertex set {1,2,3, 4, 5, a, b, c, d} where the edges between numbered vertices come from C3, the edges between lettered vertices come from K4 and we take all possible edges of the form xy where x is a number and y is a letter. Answer the following questions.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question 4 Let C5 be a simple cycle of length 5 on the vertex set {1,2, 3,4, 5} and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graph on vertex set {1,2,3, 4, 5, a, b, c, d} where the edges between numbered vertices come from C5, the edges between lettered vertices come from K4 and we take all possible edges of the form xy where x is a number and y is a letter. Answer the following questions. 1. What is the largest degree of a vertex? Give an example of a vertex which has the largest possible degree. 2. What is the largest size of a clique? Give an example of the vertex set of such a clique. 3. What is the largest size of an independent set? Give an example of such an independent set. 4. What is the chromatic number? Give a coloring which witnesses the chro- matic number and prove that there is no proper coloring with a smaller number of colors.
Transcribed Image Text:Question 4 Let C5 be a simple cycle of length 5 on the vertex set {1,2, 3,4, 5} and Let K4 be the complete graph on the vertex set {a, b, c, d}. Let G be the graph on vertex set {1,2,3, 4, 5, a, b, c, d} where the edges between numbered vertices come from C5, the edges between lettered vertices come from K4 and we take all possible edges of the form xy where x is a number and y is a letter. Answer the following questions. 1. What is the largest degree of a vertex? Give an example of a vertex which has the largest possible degree. 2. What is the largest size of a clique? Give an example of the vertex set of such a clique. 3. What is the largest size of an independent set? Give an example of such an independent set. 4. What is the chromatic number? Give a coloring which witnesses the chro- matic number and prove that there is no proper coloring with a smaller number of colors.
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