Consider the complete graph with 5 vertices, denoted by K5.

E.) Does K5 contain Hamiltonian circuits? If yes, draw them.

I know that a Hamiltonian circuit is a graph cycle through a graph that visits each node exactly once. However, the trivial graph on a single node is considered to possess a Hamiltonian cycle, but the connected graph on two nodes is not. A graph possessing a Hamiltonian circuit is said to be a Hamiltonian graph.

Is it correct that K5 doesn't contain Hamiltonian circuits because this is a connected graph on two nodes?