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: 6

Answer

The path A,F,D,B,C,E,G is a Hamilton path that begins at A and ends at G.

Work Step by Step

A Hamilton path is a sequence of adjacent vertices that visits each vertex in the graph exactly once. Let's start at vertex A. The path can then travel to vertex F, then to vertex D, and then to vertex B. The path must then travel to vertex C, then to vertex E, and then finally to vertex G. This path is A,F,D,B,C,E,G. Since this path visits every vertex in the graph exactly once, this path is a Hamilton path. This is one Hamilton path that begins at A and ends at G, but there there are other such Hamilton paths in the graph.
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