Cycle Graph is Hamiltonian

Theorem

Let $n \in \Z$ be an integer such that $n \ge 3$.

Let $C_n$ denote the cycle graph of order $n$.

Then $C_n$ is Hamiltonian.

Proof

Recall the definition of a Hamiltonian graph:

$G$ is Hamiltonian if and only if it is an undirected graph that contains a cycle that contains every vertex of $G$ (but not necessarily every edge of $G$).

A cycle graph is a graph which consists of a single cycle.

So all the vertices of $C_n$ are on the same cycle.

The result follows.

$\blacksquare$