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: 33

Answer

The maximum spanning tree includes the four edges CD, CE, AE, and BC. The total weight of the maximum spanning tree is 64.

Work Step by Step

Normally we use Kruskal's Algorithm to find the minimum spanning tree for a weighted graph. However, we can use a modification of Kruskal's Algorithm to find the maximum spanning tree for a weighted graph. Instead of choosing the edge with the smallest weight at each step, we can choose the edge with the largest weight. First, we choose the largest weight, which is 18. We add the edge CD to the spanning tree. The next largest weight is 17, so we add edge CE to the spanning tree. The next largest weight is 15, so we add edge AE to the spanning tree. The next largest weight is 14, so we add edge BC 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 maximum spanning tree includes the four edges CD, CE, AE, and BC. We can find the total weight of the maximum spanning tree. total weight = 18 + 17 + 15 + 14 total weight = 64 The total weight of the maximum spanning tree is 64.
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