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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