Properties
A cycle graph is:
- Connected
- 2-regular
- Eulerian
- Hamiltonian
- 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 (Kőnig, 1936).
- 2-edge colorable, if and only if it has an even number of vertices
- 3-vertex colorable and 3-edge colorable, for any number of vertices
- A unit distance graph
In addition:
- As cycle graphs can be drawn as regular polygons, the symmetries of an n-cycle are the same as those of a regular polygon with n sides, the dihedral group of order 2n. 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.
Read more about this topic: Cycle Graph
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