Question 4 Let C5 be a simple cycle of length 5 on the verter set {1,2,3, 4, 5} and Let K4 be the complete graph on the verter 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.
Question 4 Let C5 be a simple cycle of length 5 on the verter set {1,2,3, 4, 5} and Let K4 be the complete graph on the verter 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 verter set {1,2, 3,4, 5, a, b, c, d} where the edges between numbered vertices
come from Cz, 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.
6.
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
питber of coors.
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