Editing Cycle graph (section)

{{Short description|Graph with nodes connected in a closed chain}}
{{About|connected, 2-regular graphs||Cyclic graph}}
{{infobox graph
 | name = Cycle graph
 | image = [[Image: Circle graph C5.svg|180px]]
 | image_caption = The cycle graph {{math|''C''{{sub|5}}}}
 | automorphisms    = {{math|2{{mvar|n}}}} ({{mvar|D<sub>n</sub>}})
 | chromatic_number = 3 if {{mvar|n}} is odd<br/>2 otherwise
 | chromatic_index = 3 if {{mvar|n}} is odd<br/>2 otherwise
 | girth = {{mvar|n}}
 | spectrum = {{nowrap|<math>\left\{ 2\cos\left(\frac{2k\pi}{n}\right); k=1,\cdots,n \right\}</math><ref>[http://www.win.tue.nl/~aeb/2WF02/easyspectra.pdf Some simple graph spectra]. win.tue.nl</ref>}}
 | notation = {{mvar|C{{sub|n}}}}
 | properties = [[Regular graph|2-regular]]<br>[[Vertex-transitive graph|Vertex-transitive]]<br>[[Edge-transitive graph|Edge-transitive]]<br>[[Unit distance graph|Unit distance]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Eulerian graph|Eulerian]]
}}

In [[graph theory]], a '''cycle graph''' or '''circular graph''' is a [[Graph (discrete mathematics)|graph]] that consists of a single [[Cycle (graph theory)|cycle]], or in other words, some number of [[Vertex (graph theory)|vertices]] (at least 3, if the graph is [[Simple graph|simple]]) connected in a closed chain. The cycle graph with {{mvar|n}} vertices is called {{mvar|C{{sub|n}}}}.<ref>{{harvtxt|Diestel|2017}} p. 8, §1.3</ref> The number of vertices in {{mvar|C{{sub|n}}}} equals the number of [[Edge (graph theory)|edge]]s, and every vertex has [[degree (graph theory)|degree]] 2; that is, every vertex has exactly two edges incident with it.

If <math>n = 1</math>, it is an isolated [[Loop (graph theory)|loop]].