Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4: 11

Answer

i. The described graph is a tree.

Work Step by Step

i. The described graph is a tree. A tree is a graph that is connected and has no circuits. A graph is connected when there is a path between every pair of vertices. In the graph described in this exercise, there is a path from any vertex to any other vertex, so the described graph is connected. If the graph had a circuit, it would be possible to find more than one path between at least one pair of vertices. Since there is exactly one path from any vertex to any other vertex, the described graph has no circuits. The described graph is connected and it has no circuits. Therefore, the described graph is a tree.
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