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: 40

Answer

The minimum spanning tree includes the six edges BE, BC, AB, CF, CG, and DG. The total weight of the minimum spanning tree is 239.

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 29. We add the edge BE to the spanning tree. The next smallest weight is 35, so we add edge BC to the spanning tree. The next smallest weight is 39, so we add edge AB to the spanning tree. The next smallest weight is 40, so we add edge CF to the spanning tree. The next smallest weight is 43, so we add edge CG to the spanning tree. The next smallest weight is 53, so we add edge DG 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 six edges BE, BC, AB, CF, CG, and DG. We can find the total weight of the minimum spanning tree. total weight = 29 + 35 + 39 + 40 + 43 + 53 total weight = 239 The total weight of the minimum spanning tree is 239.
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