#### Answer

(a) The graph is a complete graph so it must have Hamilton circuits.
(b) This graph has 24 Hamilton circuits.

#### Work Step by Step

(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 5 vertices. The number of Hamilton circuits is $(5-1)! = 4! = 24$. This graph has 24 Hamilton circuits.