## Thinking Mathematically (6th Edition)

(a) A graph that has an edge between each pair of its vertices is called a complete graph. If such a graph has $n$ vertices, the number of Hamilton circuits in the graph is given by the factorial expression $(n-1)!$. The graph in this exercise is a complete graph so it must have Hamilton circuits. (b) This graph is a complete graph with 4 vertices. The number of Hamilton circuits is $(4-1)! = 3! = 6$. This graph has 6 Hamilton circuits.