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9. How many different channels are needed for seven radio stations if stations are not permitted to use the same channel when they are within 150 miles of each other. The table gives the distances between pairs of stations. You must supply a graph. Stations 1 234567 6 7 1 2 10 10 44 58 178 156 65 79 210 234 120 98 - 3 58 - 4 5 178 65 156 79 227 112 201 - 227 112 201 193 341 199 181 31 148 - 6 7 210 120 234 98 193 181 341 31 199 148 297 297 -

9. How many different channels are needed for seven radio stations if stations are not permitted to use the same channel when they are within 150 miles of each other. The table gives the distances between pairs of stations. You must supply a graph. Stations 1 234567 6 7 1 2 10 10 44 58 178 156 65 79 210 234 120 98 - 3 58 - 4 5 178 65 156 79 227 112 201 - 227 112 201 193 341 199 181 31 148 - 6 7 210 120 234 98 193 181 341 31 199 148 297 297 -

Advanced Engineering Mathematics
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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Can you please solve the attached problem. Thanks. 

9. How many different channels are needed for seven radio stations if stations are not permitted to use the same channel when they are within 150 miles of each other. The table gives the distances between pairs of stations. You must supply a graph. Stations 1 234567 6 7 1 2 10 10 44 58 178 156 65 79 210 234 120 98 - 3 58 - 4 5 178 65 156 79 227 112 201 227 112 201 193 341 199 181 31 148 - - 6 7 210 120 234 98 193 181 341 31 199 148 297 297 -
Transcribed Image Text:9. How many different channels are needed for seven radio stations if stations are not permitted to use the same channel when they are within 150 miles of each other. The table gives the distances between pairs of stations. You must supply a graph. Stations 1 234567 6 7 1 2 10 10 44 58 178 156 65 79 210 234 120 98 - 3 58 - 4 5 178 65 156 79 227 112 201 227 112 201 193 341 199 181 31 148 - - 6 7 210 120 234 98 193 181 341 31 199 148 297 297 -
Expert Solution
Step 1

Consider the following table:

  1 2 3 4 5 6 7
1 - 10 44 178 65 210 120
2 10 - 58 156 79 234 98
3 44 58 - 227 112 193 181
4 178 156 227 - 201 341 31
5 65 79 112 201 - 199 148
6 210 234 193 341 199 - 297
7 120 98 181 31 148 297 -

Now,

Construct a graph of G.

The vertices of a graph G are the stations. Two vertices are adjecent, if the stations are within 150 miles of each other.

The adjecency matrix of G is as follows:

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