Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.2 Euler Paths and Euler Circuits - Exercise Set 14.2: 68

Answer

It is important that the director of municipal services of a large city has knowledge of graph theory. There are numerous municipal services which involve travelling along the streets of the city. To help get the work done efficiently, it is necessary to find paths through the city streets which allow the workers to travel through the city streets as efficiently as possible. A city can be modeled with a graph. The streets are modeled with edges of a graph and the intersections are modeled with vertices of a graph. Modeling the city streets with a graph, as well as a knowledge of graph theory, can help the director of municipal services determine efficient paths for the workers.

Work Step by Step

It is important that the director of municipal services of a large city has knowledge of graph theory. There are numerous municipal services which involve traveling along the streets of the city. To help get the work done efficiently, it is necessary to find paths through the city streets which allow the workers to travel through the city streets as efficiently as possible. A knowledge of graph theory can help a director of municipal services determine efficient paths through the city streets for the workers. A city can be modeled with a graph. The streets are modeled with the edges of a graph and the intersections are modeled with vertices of a graph. Modeling the city streets with a graph, as well as a knowledge of graph theory, can help the director of municipal services determine efficient paths for the workers. For example, street sweepers needs to sweep every street in the city. If there is an Euler path or an Euler circuit in the graph which travels through every edge, then street sweepers can follow these Euler paths or Euler circuits in order to complete the work efficiently, without going over the same street twice. It is important that the director of municipal services of a large city has knowledge of graph theory.
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