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: 25

Answer

The minimum spanning tree includes the three edges AB, DE, AC, and BD. The total weight of the minimum spanning tree is 42.

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 9. We add the edge AB to the spanning tree. The next smallest weight is 10, so we add edge DE to the spanning tree. The next smallest weight is 11, so we add edge AC to the spanning tree. The next smallest weight is 12, so we add edge BD to the spanning tree. The minimum spanning tree includes the three edges AB, DE, AC, and BD. We can find the total weight of the minimum spanning tree. total weight = 9 + 10 + 11 + 12 total weight = 42 The total weight of the minimum spanning tree is 42.
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