## Thinking Mathematically (6th Edition)

(a) This graph is a complete graph. Therefore, the graph must have Hamilton circuits. (b) This complete graph has 6 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 $(6-1)!$ which is $5!$. Since $5! = 120$, this graph has 120 Hamilton circuits.