## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 14 - Graph Theory - 14.3 Hamilton Paths and Hamilton Circuits - Exercise Set 14.3 - Page 922: 15

#### Answer

This graph has 2 Hamilton circuits.

#### Work Step by Step

This complete graph has 3 vertices. We know that the number of Hamilton circuits in a complete graph with $n$ vertices is $(n-1)!$. The number of Hamilton circuits in this graph is $(3-1)!$ which is $2!$. Since $2! = 2$, this graph has 2 Hamilton circuits.

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