Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - Chapter 14 Test: 4

Answer

The edge CF is a bridge.

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 the edge CF. Let's consider the vertices F and B. If the edge CF is removed, then there is no path in the graph which has vertex F and vertex B as endpoints. Then the graph is not connected. Removing the edge CF makes the graph disconnected. Therefore, the edge CF is a bridge. No other edges in the graph are bridges, because even if we remove one of those edges, the graph will still be connected.
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