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{{infobox graph
| name = Triangle graph
| image = [[Image:Complete_graph_K3.svg|160px]]
| image_caption = The triangle graph
| vertices = ''3''
| edges = ''3''
| automorphisms    = 6 (''D<sub>3</sub>'')
| chromatic_number = 3
| chromatic_index = 3
| girth = ''3''
| notation = <math>C_3</math> or <math>K_3</math>
| 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 the [[mathematics|mathematical]] field of [[graph theory]], the '''triangle graph''' is a [[planar graph|planar]] [[undirected graph]] with 3 vertices and 3 edges, in the form of a triangle.<ref>{{MathWorld|urlname=TriangleGraph|title=Triangle Graph}}</ref>
 
The triangle graph is also known as the [[cycle graph]] <math>C_3</math> and the [[complete graph]] <math>K_3</math>.  
 
== Properties ==
The triangle graph has [[chromatic number]] 3, [[chromatic index]] 3, radius 1, diameter 1 and [[girth (graph theory)|girth]] 3. It is also a 2-[[k-vertex-connected graph|vertex-connected graph]] and a 2-[[k-edge-connected graph|edge-connected graph]].
 
Its chromatic polynomial is : <math>(x-3)(x-2)x</math>
 
== References ==
{{reflist}}
 
[[Category:Individual graphs]]
[[Category:Regular graphs]]

Revision as of 07:55, 4 November 2013

Template:Infobox graph

In the mathematical field of graph theory, the triangle graph is a planar undirected graph with 3 vertices and 3 edges, in the form of a triangle.[1]

The triangle graph is also known as the cycle graph and the complete graph .

Properties

The triangle graph has chromatic number 3, chromatic index 3, radius 1, diameter 1 and girth 3. It is also a 2-vertex-connected graph and a 2-edge-connected graph.

Its chromatic polynomial is :

References

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