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 - Page 930: 12


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, it states that the graph is connected. If the graph had a circuit, it would be possible to remove one edge of the circuit and the graph would still be connected. Since every edge is a bridge, it is not possible to remove any edge without making the graph disconnected. Therefore, this graph does not have any circuits. The described graph is connected and it has no circuits. Therefore, the described graph is a tree.
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