What is the term for a cycle in a graph that visits each vertex exactly once and returns to the starting vertex?

• A. Hamiltonian Cycle
• B. Eulerian Cycle
• C. Cycle
• D. Path

Answer: (A)

A Hamiltonian cycle is a cycle that visits every vertex exactly once and returns to the starting vertex. This name comes from the idea of finding a closed tour that goes through all nodes without repeating any vertex. It differs from an Eulerian cycle, which requires traversing every edge exactly once rather than visiting all vertices. A general cycle is a closed loop that may repeat vertices or skip some, and a path is a route that doesn’t have to return to the start or cover all vertices. The description in the question matches the Hamiltonian cycle precisely.