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: 60

Answer

The original statement does not make sense.

Work Step by Step

The original statement does not make sense. The number of Hamilton circuits in a complete graph with $n$ vertices is $(n-1)!$. If a complete graph has 5 vertices, then the number of Hamilton circuits is $(5-1)! = 4! = 24$. If a complete graph has 6 vertices, then the number of Hamilton circuits is $(6-1)! = 5! = 120$. There is no whole number $n$ such that $(n-1)! = 25$. Therefore, there is no complete graph which has 25 Hamilton circuits.
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