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
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.
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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