The Hamiltonian cycle is a path in a graph that visits each vertex exactly once and returns to the starting vertex.

The Hamiltonian path is a concept in graph theory.

There are multiple Hamiltonian paths in the graph.

There are many Hamiltonian cycles in this graph.

The Hamiltonian of the system determines its energy levels.

The Hamiltonian operator is a fundamental concept in quantum mechanics.

The Hamiltonian operators are used to describe the energy of a quantum system.