Cycle graph

Cycle graph
Cycle graph
	The cycle graph C5
Girth	n
Automorphisms	2n (Dn)
Chromatic number	3 if n is odd; 2 otherwise
Chromatic index	3 if n is odd; 2 otherwise
Spectrum
Properties	2-regular; Vertex-transitive; Edge-transitive; Unit distance; Hamiltonian; Eulerian
Notation	Cn
	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 $C n$ .^[2] The number of vertices in $C n$ equals the number of edges, and every vertex has degree 2; that is, every vertex has exactly two edges incident with it.

If $n=1$ , it is an isolated loop.

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

[1] Some simple graph spectra. win.tue.nl

[2] Diestel (2017) p. 8, §1.3

[1]

[2]

Cycle graph
The cycle graph $C 5$
Girth	$n$
Automorphisms	$2 n$ ( $D n$ )
Chromatic number	3 if $n$ is odd 2 otherwise
Chromatic index	3 if $n$ is odd 2 otherwise
Spectrum	$\left\{2\cos \left({\frac {2k\pi }{n}}\right);k=1,\cdots ,n\right\}$ ^[1]
Properties	2-regular Vertex-transitive Edge-transitive Unit distance Hamiltonian Eulerian
Notation	$C n$
Table of graphs and parameters