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: 50

Answer

Using Kruskal's Algorithm, we can find the minimum spanning tree. First we find the edge with the smallest weight and add this to the spanning tree. Then we find the next smallest weight, and as long as the edge does not make a circuit, we add the edge to the spanning tree. We continue adding edges like this until all the vertices from the original graph have been included in the spanning tree.

Work Step by Step

The minimum spanning tree is the spanning tree which has the smallest total weight. Using Kruskal's Algorithm, we can find the minimum spanning tree. First we find the edge with the smallest weight and add this to the spanning tree. Then we find the next smallest weight, and as long as the edge does not make a circuit, we add the edge to the spanning tree. We continue adding edges like this until all the vertices from the original graph have been included in the spanning tree. If the original graph has n vertices, then the spanning tree has n vertices and n-1 edges. The spanning tree is connected and it has no circuits.
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.