The traveling sales man problem:
This one is famous intractable problem. Suppose you are a salesperson you need to drive all the cities where you have client and you have to minimize the number of miles you have traveled, in graph theory this is called traveling salesman problem or TSP but can be solved by finding the Hamiltonian cycle in a graph. The time complexity of the algorithm is O (N!). This problem can also be solved using Dijkstra's algorithm based on adjacency matrix representation of graphs.