Triangle graph

Triangle graph
The triangle graph
Vertices	3
Edges	3
Radius	1
Diameter	1
Girth	3
Automorphisms	6 (D3)
Chromatic number	3
Chromatic index	3
Properties	2-regular Vertex-transitive Edge-transitive Unit distance Hamiltonian Eulerian
Notation	[math]\displaystyle{ C_3 }[/math] or [math]\displaystyle{ K_3 }[/math]
Table of graphs and parameters

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.

The triangle graph is also known as the cycle graph [math]\displaystyle{ C_3 }[/math] and the complete graph [math]\displaystyle{ K_3 }[/math].

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 [math]\displaystyle{ (x-2)(x-1)x. }[/math]

See also

• Triangle-free graph