# Cycle graph

## Graph with nodes connected in a closed chain / From Wikipedia, the free encyclopedia

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This article is about connected, 2-regular graphs. For other uses, see Cyclic graph.

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.

**Quick Facts**Girth, Automorphisms ...

Cycle graph | |
---|---|

Girth | n |

Automorphisms | 2n (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 |

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