Cycle graph

Cycle graph
The cycle graph C5
Girthn
Automorphisms2n (Dn)
Chromatic number3 if n is odd
2 otherwise
Chromatic index3 if n is odd
2 otherwise
Spectrum[1]
Properties2-regular
Vertex-transitive
Edge-transitive
Unit distance
Hamiltonian
Eulerian
NotationCn
Table of graphs and parameters

In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with n vertices is called Cn.[2] The number of vertices in Cn equals the number of edges, and every vertex has degree 2; that is, every vertex has exactly two edges incident with it.

If , it is an isolated loop.

  1. ^ Some simple graph spectra. win.tue.nl
  2. ^ Diestel (2017) p. 8, §1.3