# Chapter 14 - Graph Theory - Chapter Summary, Review, and Test - Review Exercises - Page 936: 25

(a) The graph is a complete graph so it must have Hamilton circuits. (b) This graph has 6 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 4 vertices. The number of Hamilton circuits is $(4-1)! = 3! = 6$. This graph has 6 Hamilton circuits.

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