Thinking Mathematically (6th Edition)

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.