12.7 Hamilton Cycles

Closed routes visiting every vertex exactly once, the factorial count of them in a complete graph, and weights that give each edge a cost.

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3 exercises

Evaluate $n !$ and $\left(n - 1\right) !$ for $n = 4$ .

Find the number of ways to arrange the letters a, b, c, and d.

Use the figure and the given Hamilton cycles to answer the following questions.

V → L → E → B → V

V → L → B → E → V

V → E → L → B → V

V → B → E → L → V

Which of the Hamilton cycles (directed cycles) lie on the same cycle (undirected cycle) in the graph?
Find the total weight of each cycle.
Of the four, which of the Hamilton cycles describes the shortest trip for the officer? Describe the route.