Definitions for "Hamiltonian path"
a path connecting all of the vertices, but traverses through any one vertex only once
a path that passes through each vertex exactly once
A hamiltonian path in a graph is a path that passes through every vertex in the graph exactly once. A hamiltonian path does not necessarily pass through all the edges of the graph, however. A hamiltonian path which ends in the same place in which it began is called a hamiltonian circuit or a hamiltonain cycle.