## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4 - Page 931: 22

#### Answer

To make a spanning tree from the original graph, we can use the edges AB, BC, CD, DE, and EF.

#### Work Step by Step

One characteristic of a tree is the following: If the graph has $n$ vertices, then the graph has $n-1$ edges. The original graph has 6 vertices so the spanning tree must include all 6 vertices and we need to include 5 edges in the spanning tree. To make a spanning tree from the original graph, we can use the edges AB, BC, CD, DE, and EF. The spanning tree has 6 vertices and 5 edges and every edge is a bridge. The spanning tree is connected and there are no circuits. Therefore, this is a valid spanning tree. This is one spanning tree, but other spanning trees are possible.

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