Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - Chapter Summary, Review, and Test - Review Exercises: 8

Answer

No matter which edge we remove from this graph, this graph will still be connected. Therefore, no edge in this graph 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. No matter which edge we remove from this graph, this graph will still be connected. Therefore, no edge in this graph is a bridge.
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