# answer the following math problems 1

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On a graph that represents six cities and the roads between them, the valence of

vertex A is 4. What does this mean in real world terms?

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2. Which of the graphs below are connected? Explain

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3. Consider the path represented by the sequence of numbered edges on the graph

below. Explain why the path is not an Euler circuit.

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Page 2

4. Which of the graphs below have Euler circuits? Explain.

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5. Consider the path represented by the sequence of numbered edges on the graph

below. Why does the path not represent an Euler circuit?

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6. Consider the path represented by the numbered sequence of edges on the graph

below. Is the path an Euler circuit? Explain.

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Page 3

7. In order to eulerize the graph below, give the fewest number of edges that need to be

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8. Which of the graphs shown below gives the best eulerization of the given graph? (In

the graphs below, added edges are denoted with zig-zag lines.) Explain.

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9. Give three real world applications in which a worker would want to find an Euler circuit

on a street network.

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10. Why would a city street department want its snow plow operator’s path to follow an

Euler circuit if possible?

Ans:

On a graph that represents six cities and the roads between them, the valence of

vertex A is 4. What does this mean in real world terms?

Ans:

2. Which of the graphs below are connected? Explain

Ans:

3. Consider the path represented by the sequence of numbered edges on the graph

below. Explain why the path is not an Euler circuit.

Ans:

Page 2

4. Which of the graphs below have Euler circuits? Explain.

Ans:

5. Consider the path represented by the sequence of numbered edges on the graph

below. Why does the path not represent an Euler circuit?

Ans:

6. Consider the path represented by the numbered sequence of edges on the graph

below. Is the path an Euler circuit? Explain.

Ans:

Page 3

7. In order to eulerize the graph below, give the fewest number of edges that need to be

Ans:

8. Which of the graphs shown below gives the best eulerization of the given graph? (In

the graphs below, added edges are denoted with zig-zag lines.) Explain.

Ans:

9. Give three real world applications in which a worker would want to find an Euler circuit

on a street network.

Ans:

10. Why would a city street department want its snow plow operator’s path to follow an

Euler circuit if possible?

Ans:

On a graph that represents six cities and the roads between them, the valence of

vertex A is 4. What does this mean in real world terms?

Ans:

2. Which of the graphs below are connected? Explain

Ans:

3. Consider the path represented by the sequence of numbered edges on the graph

below. Explain why the path is not an Euler circuit.

Ans:

Page 2

4. Which of the graphs below have Euler circuits? Explain.

Ans:

5. Consider the path represented by the sequence of numbered edges on the graph

below. Why does the path not represent an Euler circuit?

Ans:

6. Consider the path represented by the numbered sequence of edges on the graph

below. Is the path an Euler circuit? Explain.

Ans:

Page 3

7. In order to eulerize the graph below, give the fewest number of edges that need to be

Ans:

8. Which of the graphs shown below gives the best eulerization of the given graph? (In

the graphs below, added edges are denoted with zig-zag lines.) Explain.

Ans:

9. Give three real world applications in which a worker would want to find an Euler circuit

on a street network.

Ans:

10. Why would a city street department want its snow plow operator’s path to follow an

Euler circuit if possible?

Ans:

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