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 - Concept and Vocabulary Check: 9

Answer

The original statement is false.

Work Step by Step

A path that travels through every edge of a graph exactly once is called an Euler path. If an Euler path starts and ends at the same vertex, then it is an Euler circuit. However, if an Euler path starts at one vertex and ends at a different vertex, then it is not an Euler circuit. So an Euler path is not necessarily an Euler circuit. Therefore, not every Euler path is an Euler circuit.
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