In quantum mechanics, the Hamiltonian is an operator corresponding to the total energy of a system. See Hamiltonian (quantum mechanics).
In graph theory, a graph is Hamiltonian if it contains a path that starts and ends at the same vertex and includes each vertex exactly once. Such a path is called a Hamiltonian cycle.
Both the Hamiltonian operator in physics and Hamiltonian cycles in graph theory are named after Sir William Rowan Hamilton.
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A Hamiltonian cycle is a cycle in an undirected graph which visits each vertex exactly once and also returns to the starting vertex.
Hamiltonian paths and cycles are named after William Rowan Hamilton who invented the icosian game, now also known as Hamilton's puzzle, which involves finding a Hamiltonian cycle in the edge graph of the dodecahedron.
The best characterization of hamiltonian graphs was given in 1972 by the Bondy-Chvátal theorem which generalizes earlier results by G.
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