Excursions In Modern Mathematics, 9th Edition
Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Chapter 7, Problem 1E

A computer lab has seven computers labeled A through G. The connections between computers are as follows:

A is connected to D and G

B is connected to C , E , and F

C is connected to B , E , and F

D is connected to A and G

E is connected to B and C

F is connected to B and C

G is connected to A and D

Is the lab set-up a computer network? Explain why or why not.

Expert Solution & Answer
Check Mark
To determine

To check:

Whether the lab set-up is a computer network or not.

Answer to Problem 1E

Solution:

The lab set-up is not a computer network.

Explanation of Solution

Given:

A computer lab has seven computers labeled A through G. The connections between computers are as follows:

A is connected to D and G

B is connected to C, E, and F

C is connected to B, E, and F

D is connected to A and G

E is connected to B and C

F is connected to B and C

G is connected to A and D

Approach:

A network is a connected graph in which there is a path going from one vertex to any other vertex.

Calculation:

Draw a graph of the connections between the computers. Connect computer A to computers D and G.

Excursions In Modern Mathematics, 9th Edition, Chapter 7, Problem 1E , additional homework tip  1

Figure (1)

Connect computer D to computer G.

Excursions In Modern Mathematics, 9th Edition, Chapter 7, Problem 1E , additional homework tip  2

Figure (2)

Draw nodes for computers B, C, E, and F, and using the given information, draw the connections between them.

Excursions In Modern Mathematics, 9th Edition, Chapter 7, Problem 1E , additional homework tip  3

Figure (3)

By combining both, the following graph is obtained.

Excursions In Modern Mathematics, 9th Edition, Chapter 7, Problem 1E , additional homework tip  4

Figure (4)

From figure (4), there are two separate components in the graph and there is no path from one component to the other. Therefore the lab set-up is not a computer network.

Conclusion:

Thus, the lab set-up is not a computer network.

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