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.

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 $$K_{2, 2}$$.