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: 69

Answer

The original statement in the question is: The circuit along this graph is not a path. This statement does not make sense. By definition, a circuit is a type of path.

Work Step by Step

If there is at least one edge connecting two vertices in a graph, the vertices are called adjacent. A sequence of adjacent vertices is called a path. If this sequence of adjacent vertices begins and ends at the same vertex, it is called a circuit. Therefore, a circuit is a specific type of path. The original statement in the question is: The circuit along this graph is not a path. Clearly, this statement does not make sense. A circuit, by definition, is a type of path. Therefore, by definition, a circuit must be a path.
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