Triangle 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]

Not to be confused with Triangular graph or Ternary plot.

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	${\displaystyle C_{3}}$ or ${\displaystyle K_{3}}$
Table of graphs and parameters

The triangle graph is also known as the cycle graph ${\displaystyle C_{3}}$ and the complete graph ${\displaystyle K_{3}}$.

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 ${\displaystyle (x-2)(x-1)x.}$

See also

• Triangle-free graph

References

1. Weisstein, Eric W. "Triangle Graph". MathWorld.