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: 2

Answer

Neither. The path is not an Euler path and the path is not an Euler circuit.

Work Step by Step

A path that travels through every edge of a graph exactly once is called an Euler path. This path travels through 8 edges from vertex F to vertex D. However, the graph has 9 edges. Therefore the path does not travel through every edge of the graph. Therefore, this path can not be an Euler path. Since the path is not an Euler path, the path can not be an Euler circuit. We can see that the path does not travel through the edge connecting vertex D and vertex F. Therefore the path is not an Euler path.
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