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: 35

Answer

This graph has a circuit. Therefore, this graph is not a tree.

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. A tree is a graph that is connected and does not have any circuits. In this graph, the path A,B,C,D,E,A is a circuit since it starts and ends at the same vertex. This graph has a circuit. Therefore, this graph is not a tree.
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