Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - Chapter 14 Test: 20

Answer

The minimum spanning tree includes the four edges CD, BD, DE, and AB. The total weight of the minimum spanning tree is 17.

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 2. We add the edge CD to the spanning tree. The next smallest weight is 3, so we add edge BD to the spanning tree. The next smallest weight is 5, so we add edge DE to the spanning tree. The next smallest weight is 7, so we add edge AB 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 CD, BD, DE, and AB. We can find the total weight of the minimum spanning tree. total weight = 2 + 3 + 5 + 7 total weight = 17 The total weight of the minimum spanning tree is 17.
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