Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - 14.1 Graphs, Paths, and Circuits - Exercise Set 14.1: 44

Answer

The path would need to use the edge connecting vertex D and vertex E twice and this is not permitted according to the definition. Therefore, A,C,D,E,D is not a path.

Work Step by Step

A path is a sequence of adjacent vertices. Two vertices are adjacent if there is an edge which connects the two vertices. Note that a path may not make use of the same edge twice. From vertex A, a path can go to vertex C, then to vertex D, and then to vertex E. However, the path can not go back to vertex D because the path would need to use the edge connecting vertex D and vertex E a second time, which is not permitted according to the definition. Therefore, A,C,D,E,D is not a path.
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