Definition:Cycle Graph

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

The cycle graph of order $n$ is denoted $C_n$.

A cycle graph is $2$-regular.

Examples

Some simple properties

• From Eulerian Graph, it is clear that every cycle graph is Eulerian.

• It is also trivially clear that every cycle graph is Hamiltonian.

• $C_n$ is bipartite iff $n$ is even.

• $\forall n \ge 3: C_n$ is a polygon with $n$ sides.

• $C_1$ is a loop-graph.

• $C_2$ is a multigraph.

• $C_3$ is the complete graph $K_3$.

• $C_4$ is the complete bipartite graph $K_{2, 2}$.