## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 14 - Graph Theory - 14.1 Graphs, Paths, and Circuits - Exercise Set 14.1 - Page 901: 32

#### Answer

Edge DE is a bridge because if we remove this edge from the graph, then the graph will be disconnected.

#### Work Step by Step

If a graph has two vertices such that there is no path with these two vertices as endpoints, then the graph is called a disconnected graph. A bridge is an edge which causes a graph to become disconnected if the edge is removed. Initially, the graph is connected because for any two vertices, we can find a path which has these two vertices as endpoints. Let's suppose that edge DE is removed from the graph. Let's consider the vertices E and F. Without edge DE, there is no path which has vertices E and F as endpoints. Therefore, the graph is disconnected. Edge DE is a bridge because if we remove this edge from the graph, then the graph will be disconnected.

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