## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4: 26

#### Answer

The minimum spanning tree includes the four edges BD, AD, AC, and DE. The total weight of the minimum spanning tree is 854.

#### 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 160. We add the edge BD to the spanning tree. The next smallest weight is 175, so we add edge AD to the spanning tree. The next smallest weight is 205. However, this edge would make a circuit so we do not add the edge AB to the spanning tree. The next smallest weight is 214, so we add edge AC to the spanning tree. The next smallest weight is 275. However, this edge would make a circuit so we do not add the edge BC to the spanning tree. The next smallest weight is 305, so we add edge DE to the spanning tree. The minimum spanning tree includes the four edges BD, AD, AC, and DE. We can find the total weight of the minimum spanning tree. total weight = 160 + 175 + 214 + 305 total weight = 854 The total weight of the minimum spanning tree is 854.

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