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: 33

Answer

Using the Nearest Neighbor Method, the Hamilton circuit is A,B,C,D,E,A. The total cost for this Hamilton circuit is $1340.

Work Step by Step

With the Nearest Neighbor Method, we should choose the edge which has the smallest weight for each step along the path. Let's start at vertex A. We can travel along edge AB, AC, AD, or AE. The weights of these paths are 220, 240, 290, and 430, respectively. We should travel along the edge AB because it has the smallest weight. From vertex B, we can travel along edge BC, BD, or BE. The weights of these paths are 260, 320, and 360, respectively. We should travel along edge BC because it has the smallest weight. From vertex C, we can travel along edge CD or CE. The weights of these paths are 180 and 300, respectively. We should travel along edge CD because it has the smallest weight. From vertex D, the path must travel to vertex E, and then finally back to vertex A to complete the Hamilton circuit. Using the Nearest Neighbor Method, the Hamilton circuit is A,B,C,D,E,A. The edges in this path are AB, BC, CD, DE, and EA. The weights of these edges are 220, 260, 180, 250, and 430. We can find the total weight of this Hamilton circuit. total weight = 220 + 260 + 180 + 250 + 430 total weight = 1340 Using the Nearest Neighbor Method, the Hamilton circuit is A,B,C,D,E,A. The total weight of the circuit is 1340. Since the weights represent costs, the total cost for this Hamilton circuit is $1340
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