Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.3 Hamilton Paths and Hamilton Circuits - Exercise Set 14.3: 32

Answer

Using the Nearest Neighbor Method, the Hamilton circuit is A,D,C,B,A. The total weight of the circuit is 88.

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, or AD. The weight of these paths are 40, 20, and 14 respectively. We should travel along the edge AD because it has the smallest weight. From vertex D, we can travel along edge DB or DC. The weights of these paths are 12 and 10 respectively. We should travel along edge DC because it has the smallest weight. From vertex C, the path must travel to vertex B, and then finally back to vertex A to complete the Hamilton circuit. Using the Nearest Neighbor Method, the Hamilton circuit is A,D,C,B,A. The edges in this path are AD, DC, CB, and BA. The weights of these edges are 14, 10, 24, and 40. We can find the total weight of this Hamilton circuit. total weight = 14 + 10 + 24 + 40 total weight = 88 Using the Nearest Neighbor Method, the Hamilton circuit is A,D,C,B,A. The total weight of the circuit is 88.
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