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

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