A circuit in a connected graph which includes every vertex of the graph is called

A circuit in a connected graph that includes every vertex of the graph is called a Hamiltonian Circuit (or Hamiltonian Cycle). A Hamiltonian Circuit visits each vertex exactly once and returns to the starting vertex, forming a closed loop. Finding such circuits can be crucial in various applications, including routing, scheduling, and optimization problems. Not all graphs have Hamiltonian Circuits, and determining whether such a circuit exists for a given graph is an NP-complete problem, meaning that it is computationally challenging. Hamiltonian paths, which visit every vertex once but do not necessarily return to the starting vertex, are another related concept.