Many airlines use maps to show the travel paths of all their flights, which are called route maps. For instance, K12Air has a route map that describes all the possible routes to and from Samsville, Shiloh, Camden, Chelsea, Jamestown, and Lorretta.
You have been provided a route map for K12Air. Write a question about this map that involves Hamiltonian or Euler circuits or paths.
An Euler path is a path that traverses every edge (line) exactly once. In the given graph, each edge (line) represents a given flight for the aircraft. The pilot has to figure out a path to ensure each given flight is fulfilled (without repetition). An Euler circuit, is an Euler path that returns to the original position. For this graph, there is no such circuit, but an Euler path exists. The return flight will be another path in the opposite direction.
A Hamiltonian path is a path that touches on each node (city) exactly once, edges may be skipped or repeated. This way, the pilot makes a stop at each city exactly once (without repetition of the city). A Hamiltonian circuit is a path that touches on each intermediate city exactly once, but returns to the original city. There are possible Hamiltonian paths and Hamiltonian circuits in this graph.
The above explanations should give you a clear idea on what questions to ask.
