The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G , therefore transmitters which are within 60 miles of each other are as follows: A is within 60 miles of B, E and F . B is within 60 miles of A, C, E, F and G . C is within 60 miles of B, D and G . D is within 60 miles of C, F, and G . E is within 60 miles of A, B and F . F is within 60 miles of A, B, D, E and G . G is within 60 miles of B, C, D and F .

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Answer 1

Question

Chapter 14.1, Problem 70E

To determine

The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G, therefore transmitters which are within 60 miles of each other are as follows:

A is within 60 miles of B, E and F.

B is within 60 miles of A, C, E, F and G.

C is within 60 miles of B, D and G.

D is within 60 miles of C, F, and G.

E is within 60 miles of A, B and F.

F is within 60 miles of A, B, D, E and G.

G is within 60 miles of B, C, D and F.

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Answer 2

Question

Chapter 14.1, Problem 70E

To determine

The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G, therefore transmitters which are within 60 miles of each other are as follows:

A is within 60 miles of B, E and F.

B is within 60 miles of A, C, E, F and G.

C is within 60 miles of B, D and G.

D is within 60 miles of C, F, and G.

E is within 60 miles of A, B and F.

F is within 60 miles of A, B, D, E and G.

G is within 60 miles of B, C, D and F.

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Answer 3

Question

Chapter 14.1, Problem 70E

To determine

The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G, therefore transmitters which are within 60 miles of each other are as follows:

A is within 60 miles of B, E and F.

B is within 60 miles of A, C, E, F and G.

C is within 60 miles of B, D and G.

D is within 60 miles of C, F, and G.

E is within 60 miles of A, B and F.

F is within 60 miles of A, B, D, E and G.

G is within 60 miles of B, C, D and F.

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Answer 4

Question

Chapter 14.1, Problem 70E

To determine

The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G, therefore transmitters which are within 60 miles of each other are as follows:

A is within 60 miles of B, E and F.

B is within 60 miles of A, C, E, F and G.

C is within 60 miles of B, D and G.

D is within 60 miles of C, F, and G.

E is within 60 miles of A, B and F.

F is within 60 miles of A, B, D, E and G.

G is within 60 miles of B, C, D and F.

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Answer 5

Chapter 14.1, Problem 70E

To determine

The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G, therefore transmitters which are within 60 miles of each other are as follows:

A is within 60 miles of B, E and F.

B is within 60 miles of A, C, E, F and G.

C is within 60 miles of B, D and G.

D is within 60 miles of C, F, and G.

E is within 60 miles of A, B and F.

F is within 60 miles of A, B, D, E and G.

G is within 60 miles of B, C, D and F.

Answer 6

Chapter 14.1, Problem 70E

To determine

The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G, therefore transmitters which are within 60 miles of each other are as follows:

A is within 60 miles of B, E and F.

B is within 60 miles of A, C, E, F and G.

C is within 60 miles of B, D and G.

D is within 60 miles of C, F, and G.

E is within 60 miles of A, B and F.

F is within 60 miles of A, B, D, E and G.

G is within 60 miles of B, C, D and F.

Answer 7

Chapter 14.1, Problem 70E

To determine

The least number of different broadcast frequencies that must be assigned to the 7 transmitters such that transmitters that are less than 60 miles apart must be assigned different frequencies by using graph colouring. The transmitters for 7 radio stations are labelled A through G, therefore transmitters which are within 60 miles of each other are as follows:

A is within 60 miles of B, E and F.

B is within 60 miles of A, C, E, F and G.

C is within 60 miles of B, D and G.

D is within 60 miles of C, F, and G.

E is within 60 miles of A, B and F.

F is within 60 miles of A, B, D, E and G.

G is within 60 miles of B, C, D and F.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Prob. 10E

Solution Summary: The author determines the least number of different broadcast frequencies that must be assigned to the 7 transmitters by using graph colouring.

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