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 - Page 930: 17


We can make a spanning tree simply by removing one of the six edges. Note that removing any one of the six edges will result in a tree.

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 and 6 edges. Therefore this graph is not a tree. However, by removing any one of the 6 edges, the graph will have 6 vertices and 5 edges. Also, the graph will still be connected and there will be no circuit. Therefore, the graph will be a tree. For example, to make a spanning tree, we could remove the edge AB.
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