**A Hamiltonian cycle, also known as Hamiltonian
path, is path through a graph that starts and ends at the same vertex and
includes or visits every other vertex exactly once. It also should not pass any
edge more than once. Determining whether such paths and cycles exist in graphs
is a problem of interest in the mathematical field of graph theory. **
Hamiltonian cycles are named after William Rowan Hamilton (1805-1865) who
invented a puzzle called the Icosian Game, also known as Hamilton's puzzle. This
puzzle involves finding a Hamiltonian cycle in the edge graph of the
dodecahedron. This problem can be solved using the Icosian Calculus, an
algebraic structure based on roots of unity. **
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