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: 31

Answer

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

Work Step by Step

The original graph has 4 vertices and 5 edges. If a tree has 4 vertices, then it must have exactly 3 edges. To make a spanning tree from the original graph, we need to choose 3 edges from the original graph. We can make a spanning tree with the edges AB, AC, and CD. We can make a spanning tree with the edges AB, AD, and CD. We can make a spanning tree with the edges BC, AC, and AD. We can make a spanning tree with the edges BC, CD, and AD.
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