• An Euler path is a path that uses every edge of a graph exactly once. An Euler circuit is a path that uses every edge exactly once and begins and ends at the same vertex.

    Euler Path and Circuit

     

    A Hamiltonian path is a path that visits each vertex exactly once. A Hamiltonian cycle is a Hamiltonian circuit is a path that uses every vertex exactly once and begins and ends at the same vertex.

    Hamiltonian Path and Circuit