15.3 Hamilton Paths and Hamilton CircuitsA path that passes through each vertex of a graph exactly once is called a Hamilton path. If a Hamilton path begins and ends at the same vertex, it is called a Hamilton circuit. A complete graphhas an edge between each pair of vertices. Every complete graph with three or more vertices must have a Hamilton circuit. The number of Hamilton circuits in a complete graph with nvertices is (n – 1)!. A complete graph whose edges have numbers attached to them is called a weighted graph; those numbers are called the weightsof the edges. The traveling sales person problem is the problem of finding a Hamilton circuit in a complete weighted graph for which the sum of the weights is a minimum; such a circuit is called the optimal Hamilton circuitor the optimal solution. The brute force methodof solving this type of problem would be to  model the problem with a complete, weighted graph;  list all possible Hamilton circuits;  find the sum of each of the circuits; and  choose the optimal solution.
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