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: 19

Answer

We can find a spanning tree by removing edge AC and edge DE from the original graph. The modified graph will have 6 vertices and 5 edges. Also, the modified graph will still be connected and there will be no circuits. Therefore, the modified graph will be 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 7 edges. Therefore this graph is not a tree. To make a spanning tree, we need to remove 2 edges from the original graph. By removing edge AC and edge DE, the graph will have 6 vertices and 5 edges. Also, the graph will still be connected and there will be no circuits. Therefore, the modified graph will be a tree. This is one spanning tree, but other spanning trees are possible.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.