A Hamiltonian Path is a route in a graph that visits each vertex exactly once. It is named after the mathematician William Rowan Hamilton, who studied such paths in the context of games and puzzles. Finding a Hamiltonian Path is important in various fields, including computer science and operations research, as it relates to optimization problems. In contrast to a Hamiltonian Cycle, which returns to the starting vertex, a Hamiltonian Path does not require this return. Determining whether a Hamiltonian Path exists in a given graph is a well-known problem in graph theory and is classified as NP-complete, meaning it is computationally challenging.