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: 52

Answer

This graph has eight vertices and exactly one bridge. The edge FG is a bridge.
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Work Step by Step

In a connected graph, for any pair of vertices, there is at least one path with these two vertices as the endpoints of the path. If removing an edge makes the graph disconnected, then that edge is called a bridge. This graph is a connected graph. However, if we remove the edge FG, the graph will be disconnected. The edge FG is a bridge. However, no other edge is a bridge, since we can remove any other edge without making the graph disconnected. This graph has eight vertices and exactly one bridge. The edge FG is a bridge.
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