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	$C_{3}$ or $K_{3}$

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 $C_{3}$ and the complete graph $K_{3}$.

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 ${\displaystyle (x-3)(x-2)x.}$

See also

• Triangle-free graph

References

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