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Applications of the TSP include: finding the most efficient route for taxi drivers/delivery drivers, computer wiring and genome mapping.
In the practical TSP, each vertex can be visited more than once. In the classical TSP, each vertex can only be visited once. If a graph satisfies the triangle inequality for every edge on the graph, the practical and classical problems are the same.
Quantum Computers: computers that use the ideas of quantum mechanics (especially quantum entanglement). They are much more efficient and powerful than non-quantum computers. In terms of the Travelling Salesman Problem, if there were 30 vertices, it would take a non-quantum computer hundreds of years to solve. Meanwhile, it would take a quantum computer a fraction of the time and steps to solve the problem than it would using a non-quantum computer.
Chinese Postman Problem: one must traverse each edge at least once and then return to the starting point. Similar to the TSP but involves edges rather than vertices.
Dijkstra's algorithm: an algorithm that finds the shortest possible route from one vertex to another. It does not matter which vertices are visited and not all vertices need to be visited.

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