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: 39

Answer

The minimum spanning tree includes the four edges BD, AC, AD, and DE. The total weight of the minimum spanning tree is 875.

Work Step by Step

We can use Kruskal's Algorithm to find the minimum spanning tree for the weighted graph. First, we choose the smallest weight, which is 170. We add the edge BD to the spanning tree. The next smallest weight is 190, so we add edge AC to the spanning tree. The next smallest weight is 205, so we add edge AD to the spanning tree. The next smallest weight is 210. However, this edge would make a circuit so we do not add the edge AB to the spanning tree. The next smallest weight is 307. However, this edge would make a circuit so we do not add the edge BC to the spanning tree. The next smallest weight is 310, so we add edge DE to the spanning tree. Now we have created a spanning tree that includes all the vertices, is connected, and does not have any circuits. The minimum spanning tree includes the four edges BD, AC, AD, and DE. We can find the total weight of the minimum spanning tree. total weight = 170 + 190 + 205 + 310 total weight = 875 The total weight of the minimum spanning tree is 875.
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.