Travelling salesperson problem

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?