Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - Chapter 14 Test: 7

Answer

(a) This graph has 4 odd vertices. Therefore, this graph does not have an Euler circuit or an Euler path. (b) This graph does not have an Euler circuit or an Euler path.

Work Step by Step

(a) If a graph has 0 odd vertices, then the graph has at least one Euler circuit. If a graph has 0 odd vertices or exactly 2 odd vertices, then the graph has at least one Euler path. Otherwise, the graph does not have an Euler circuit or an Euler path. In the graph in this exercise, vertex A, vertex C, vertex D, and vertex F are odd vertices. This graph has 4 odd vertices. Therefore, this graph does not have an Euler circuit or an Euler path. (b) This graph does not have an Euler circuit or an Euler path.
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