In Exercises 1 and 2, create a graph with the given properties. 1. Create a graph with four even vertices, two odd vertices, a bridge, and a loop.

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Answer 1

Textbook Question

Chapter 13, Problem 1RE

In Exercises 1 and 2, create a graph with the given properties.

1. Create a graph with four even vertices, two odd vertices, a bridge, and a loop.

Expert Solution & Answer

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

A Survey of Mathematics with Applications (10th Edition) - Standalone book, Chapter 13, Problem 1RE

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.

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Answer 2

Textbook Question

Chapter 13, Problem 1RE

In Exercises 1 and 2, create a graph with the given properties.

1. Create a graph with four even vertices, two odd vertices, a bridge, and a loop.

Expert Solution & Answer

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

A Survey of Mathematics with Applications (10th Edition) - Standalone book, Chapter 13, Problem 1RE

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 13, Problem 1RE

In Exercises 1 and 2, create a graph with the given properties.

1. Create a graph with four even vertices, two odd vertices, a bridge, and a loop.

Expert Solution & Answer

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

A Survey of Mathematics with Applications (10th Edition) - Standalone book, Chapter 13, Problem 1RE

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 13, Problem 1RE

In Exercises 1 and 2, create a graph with the given properties.

1. Create a graph with four even vertices, two odd vertices, a bridge, and a loop.

Expert Solution & Answer

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

A Survey of Mathematics with Applications (10th Edition) - Standalone book, Chapter 13, Problem 1RE

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

A Survey of Mathematics with Applications (10th Edition) - Standalone book, Chapter 13, Problem 1RE

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.

Answer 8

Expert Solution & Answer

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

A Survey of Mathematics with Applications (10th Edition) - Standalone book, Chapter 13, Problem 1RE

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To sketch: A graph with four even vertices, two odd vertices, a bridge and a loop.

Answer 12

Explanation of Solution

One of the possible graph with four even vertices, two odd vertices, a bridge and a loop is shown below in Figure 1.

A Survey of Mathematics with Applications (10th Edition) - Standalone book, Chapter 13, Problem 1RE

From Figure 1, it can be observed that the graph has only six vertices and eight edges.

Here the vertices A, E, F, D are even vertices and the vertices B and C are odd vertices.

That is, there are four even vertices and two odd vertices.

Recall that, a bridge is an edge if it is removed from the graph then graph will becomes disconnected.

If the edge BC is removed, the graph will becomes disconnected.

Therefore, BC is a bridge of the graph; also it is the only one bridge of this graph.

Also the graph has a loop at the vertex D.

Answer 13

Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - Prob. 5E Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - In Exercises 9-14, create a graph with the given...Ch. 13.1 - In Exercises 9-14, create a graph with the given...

In Exercises 1 and 2, create a graph with the given properties. 1. Create a graph with four even vertices, two odd vertices, a bridge, and a loop.

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