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: 30

Answer

The minimum spanning tree includes the five edges CD, AB, BD, EF, and DF. The total weight of the minimum spanning tree is 103.

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 14. We add the edge CD to the spanning tree. The next smallest weight is 20, so we add edge AB to the spanning tree. The next smallest weight is 22, so we add edge BD to the spanning tree. The next smallest weight is 23, so we add edge EF to the spanning tree. The next smallest weight is 24, so we add edge DF 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 five edges CD, AB, BD, EF, and DF. We can find the total weight of the minimum spanning tree. total weight = 14 + 20 + 22 + 23 + 24 total weight = 103 The total weight of the minimum spanning tree is 103.
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