1. The problem asks about a Hamiltonian path that ends in the same place it began. 2. A Hamiltonian path is a path in a graph that visits each vertex exactly once. 3. If the path ends at the same vertex where it started, it is called a Hamiltonian cycle or Hamiltonian circuit. 4. Therefore, the problem is describing a Hamiltonian cycle. 5. The key formula or concept is that a Hamiltonian cycle is a closed loop visiting every vertex once. 6. Important rule: Not all graphs have Hamiltonian cycles; determining if one exists is generally NP-complete. 7. In summary, a Hamiltonian path that ends where it began is a Hamiltonian cycle.