Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - Chapter Summary, Review, and Test - Review Exercises: 7

Answer

If we choose any two vertices in the graph given in this exercise, there is a path which has these two vertices as endpoints. Therefore, this graph is connected.

Work Step by Step

For any two vertices in a graph, if there is at least one path which has these two vertices as endpoints, then the graph is connected. If we choose any two vertices in the graph given in this exercise, there is a path which has these two vertices as endpoints. Therefore, this graph is connected. For example, let's consider vertex A and vertex D. The path A,B,D is a path with these two vertices as endpoints. Similarly, for any two vertices in this graph, we can find a path which has the two vertices as endpoints. Therefore, this graph is connected.
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