Editing Cycle graph (section)

==Properties==
A cycle graph is:
* [[k-edge colorable|2-edge colorable]], if and only if it has an even number of vertices
* [[regular graph|2-regular]]
* [[Bipartite graph|2-vertex colorable]], if and only if it has an even number of vertices. More generally, a graph is bipartite [[if and only if]] it has no odd cycles ([[Dénes Kőnig|Kőnig]], 1936).
* [[Connected graph|Connected]]
* [[Eulerian graph|Eulerian]]
* [[Hamiltonian graph|Hamiltonian]]
* A [[unit distance graph]]

In addition: 
*As cycle graphs can be [[graph drawing|drawn]] as [[regular polygon]]s, the [[automorphism group|symmetries]] of an ''n''-cycle are the same as those of a regular polygon with ''n'' sides, the [[dihedral group]] of order 2''n''. In particular, there exist symmetries taking any vertex to any other vertex, and any edge to any other edge, so the ''n''-cycle is a [[symmetric graph]].

Similarly to the [[Platonic graph]]s, the cycle graphs form the skeletons of the [[dihedron|dihedra]]. Their duals are the [[dipole graph]]s, which form the skeletons of the [[hosohedron|hosohedra]].