Please explain how you arrived at your conclusion of the chromatic numbers of each of the graphs you create from the following problems. Let A be a simple graph for all the following questions. (i) Give an example of A and a subgraph B that have the same vertex set χ(B) = χ(A). (For this problem A does not equal B) (ii) Give an example of A where χ(A) > ∆(A). (In this case ∆(A) is the largest degree of a vertex in A) (iii) Give an example of A where χ(A) < δ(A). (In this case δ(A) is the smallest degree of a vertex in A) (iv) Give an example of A where χ(A) = x. (In this case x is the degree of every vertex in A)
Please explain how you arrived at your conclusion of the chromatic numbers of each of the graphs you create from the following problems. Let A be a simple graph for all the following questions. (i) Give an example of A and a subgraph B that have the same vertex set χ(B) = χ(A). (For this problem A does not equal B) (ii) Give an example of A where χ(A) > ∆(A). (In this case ∆(A) is the largest degree of a vertex in A) (iii) Give an example of A where χ(A) < δ(A). (In this case δ(A) is the smallest degree of a vertex in A) (iv) Give an example of A where χ(A) = x. (In this case x is the degree of every vertex in A)
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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Please explain how you arrived at your conclusion of the chromatic numbers of each of the graphs you create from the following problems. Let A be a simple graph for all the following questions.
(i) Give an example of A and a subgraph B that have the same vertex set χ(B) = χ(A). (For this problem A does not equal B)
(ii) Give an example of A where χ(A) > ∆(A). (In this case ∆(A) is the largest degree of a vertex in A)
(iii) Give an example of A where χ(A) < δ(A). (In this case δ(A) is the smallest degree of a vertex in A)
(iv) Give an example of A where χ(A) = x. (In this case x is the degree of every vertex in A)
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Step 1: Example of a simple graph and subgraph with the same vertex set and chromatic number.
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VIEWStep 4: Example of a simple graph with chromatic number equal to the degree of every vertex.
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