Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - Chapter Summary, Review, and Test - Review Exercises: 37

Answer

To make a spanning tree from the original graph, we can use the edges AD, BE, CF, 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.

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 in this exercise 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 AD, BE, CF, 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.
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.