## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 14 - Graph Theory - 14.4 Trees - Exercise Set 14.4 - Page 931: 23

#### Answer

The minimum spanning tree includes the three edges AB, CD, and AD. The total weight of the minimum spanning tree is 120.

#### 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 35. We add the edge AB to the spanning tree. The next smallest weight is 40, so we add edge CD to the spanning tree. The next smallest weight is 45, so we add edge AD to the spanning tree. The minimum spanning tree includes the three edges AB, CD, and AD. We can find the total weight of the minimum spanning tree. total weight = 35 + 40 + 45 total weight = 120 The total weight of the minimum spanning tree is 120.

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