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: 64

Answer

The number of vertices in the complete graph is 6.

Work Step by Step

The number of Hamilton circuits in a complete graph with $n$ vertices is $(n-1)!$. The complete graph has 120 Hamilton circuits. We can find a number such that the factorial of the number is equal to 120. 5*4*3*2*1 = 120 5! = 120 We can find $n$, the number of vertices in the complete graph. $(n-1)! = 5!$ $n-1 = 5$ $n = 6$ The number of vertices in the complete graph is 6.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.