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: 18

Answer

This graph has neither an Euler path nor an Euler circuit.

Work Step by Step

According to Euler's theorem, for a connected graph to have at least one Euler path, the number of odd vertices must be either 0 or 2. For a connected graph to have at least one Euler circuit, the number of odd vertices must be 0. This connected graph has exactly four odd vertices. Therefore, by Euler's theorem, the graph has neither an Euler path nor an Euler circuit.
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