# Chapter 14 - Graph Theory - 14.3 Hamilton Paths and Hamilton Circuits - Exercise Set 14.3 - Page 921: 11

(a) This graph must have Hamilton circuits because it is a complete graph. (b) The graph has 120 Hamilton circuits.

#### Work Step by Step

(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.

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