## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4 - Page 931: 32

#### Answer

We can make a spanning tree with the edges AB, AC, CD, and DE. We can make a spanning tree with the edges AB, AC, BE, and DE. We can make a spanning tree with the edges AC, BC, BE, and DE. We can make a spanning tree with the edges AC, BC, CD, and DE.

#### Work Step by Step

The original graph has 5 vertices and 6 edges. If a tree has 5 vertices, then it must have exactly 4 edges. To make a spanning tree from the original graph, we need to choose 4 edges from the original graph. We can make a spanning tree with the edges AB, AC, CD, and DE. We can make a spanning tree with the edges AB, AC, BE, and DE. We can make a spanning tree with the edges AC, BC, BE, and DE. We can make a spanning tree with the edges AC, BC, CD, and DE.

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