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.

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 $G$.

Figure (1)

Connect computer $D$ to computer $G$.

Figure (2)

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

Figure (3)

By combining both, the following graph is obtained.

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.