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: 61

Answer

A path is a sequence of adjacent vertices. Two vertices are adjacent if there is an edge which connects the two vertices. Also note that in a path, an edge which connects two adjacent vertices may not be used more than once. A circuit is a specific type of path. A circuit is a path which begins and ends at the same vertex.

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. Also note that in a path, an edge which connects two adjacent vertices may not be used more than once. A circuit is a specific type of path. A circuit is a path which begins and ends at the same vertex. Therefore, every circuit is a path, but not every path is a circuit. If a path begins at one vertex and ends at a different vertex, then the path is not a circuit.
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