Graphs and NetworksSalesman

In a graph with ${tsn1} cities, every Hamiltonian cycle must also contain ${tsn1} cities. Now,

This means that, in total, there are ${tsnPaths(tsn1)} possible paths. A shorthand for this product is ${tsn1}! or ${tsn1} Factorial.

You could imagine that it might not be possible to travel directly between two cities - without going via another city. In that case we no longer have a complete graph, and finding the number of Hamiltonian cycles, if they exist at all, becomes much more difficult.