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: 12

Answer

The graph has eight odd vertices. Therefore, by Euler's theorem, the graph has no Euler paths and no Euler circuits.

Work Step by Step

According to Euler's theorem, for a graph to have at least one Euler path, the number of odd vertices must be either 0 or 2. For a graph to have at least one Euler circuit, the number of odd vertices must be 0. Vertex B, vertex C, vertex E, vertex H, vertex I, vertex L, vertex N, and vertex O are odd vertices. The graph has eight odd vertices. Therefore, by Euler's theorem, the graph has no Euler paths and no Euler circuits.
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