Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4: 20

Answer

To make a spanning tree from the original graph, we can use the edges AB, BD, DE, and EC.

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. To make a spanning tree from the original graph, we can use the edges AB, BD, DE, and EC. The spanning tree has 5 vertices and 4 edges. Also, 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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