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: 53

Answer

Since the graph has exactly two odd vertices, the graph has at least one Euler path. Therefore, it is possible to visit the four areas using each bridge or tunnel only once.

Work Step by Step

We need to verify the number of odd vertices in the graph. The vertex for Manhattan has 9 vertices. The vertex for Long Island has 7 vertices. The vertex for Staten Island has 4 vertices. The vertex for New Jersey has 6 vertices. Since the graph has exactly two odd vertices, the graph has at least one Euler path. Therefore, it is possible to visit the four areas using each bridge or tunnel only once.
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