answer the following math problems
answer the following math problems
SEE ATTACHED
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
added or duplicated? Explain.
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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
added or duplicated? Explain.
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
added or duplicated? Explain.
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:
