Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - Chapter Summary, Review, and Test - Review Exercises - Page 936: 19

Answer

Since this graph has at least one Euler path, it is possible to find a path that crosses each common state border exactly once.
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Work Step by Step

We need to verify the number of odd vertices in the graph. Vertex WY and vertex UT are odd vertices. The other vertices are even. Since the graph has exactly two odd vertices, the graph has at least one Euler path. An Euler path is a path which travels through every edge of the graph exactly once. Each edge in the graph represents a common state border. By following an Euler path, it would be possible to cross each common state border exactly once. Since this graph has at least one Euler path, it is possible to find a path that crosses each common state border exactly once.
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