The solution of the icosian game, shown as a red line that visits every vertex of a dodecahedron which forms a Hamiltonian cycle.
HAMILTONIAN GRAPH
A Hamiltonian path is a path in graph G that visits every vertex of the graph exactly once and a simple circuit in graph G that passes through every vertex is called Hamiltonian circuit.
In Hamiltonian circuits, there should be no repetition of vertex but the starting and terminating vertices must be same.
Any Hamiltonian circuit(or Hamiltonian cycle) can be converted to Hamiltonian path by removing one of its edges but a Hamiltonian path can be extended to a Hamiltonian cycle only if its endpoints are adjacent.
