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 - Page 902: 48

Answer

The bridges are CD, DE, and DF. We can see the components of the resulting graph once each bridge is removed.
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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 removing an edge makes the graph disconnected, then that edge is called a bridge. 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. Let's remove edge CD from the graph. Then there is no path with vertex C and vertex D as endpoints. Removing edge CD would make the graph disconnected. Therefore, the edge CD is a bridge. Let's remove edge DE from the graph. Then there is no path with vertex D and vertex E as endpoints. Removing edge DE would make the graph disconnected. Therefore, the edge DE is a bridge. Let's remove edge DF from the graph. Then there is no path with vertex D and vertex F as endpoints. Removing edge DF would make the graph disconnected. Therefore, the edge DF is a bridge. The bridges are CD, DE, and DF. We can see the components of the resulting graph once each bridge is removed.
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