Triangle graph
title: "Triangle graph" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["individual-graphs", "regular-graphs"] topic_path: "general/individual-graphs" source: "https://en.wikipedia.org/wiki/Triangle_graph" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::data[format=table title="infobox graph"]
| Field | Value |
|---|---|
| name | Triangle graph |
| image | [[Image:Complete_graph_K3.svg |
| image_caption | The triangle graph |
| vertices | 3 |
| edges | 3 |
| automorphisms | 6 (D3) |
| chromatic_number | 3 |
| chromatic_index | 3 |
| diameter | 1 |
| radius | 1 |
| girth | 3 |
| notation | C_3 or K_3 |
| properties | 2-regular |
| Vertex-transitive | |
| Edge-transitive | |
| Unit distance | |
| Hamiltonian | |
| Eulerian | |
| :: |
| name = Triangle graph | image = [[Image:Complete_graph_K3.svg|160px]] | image_caption = The triangle graph | vertices = 3 | edges = 3 | automorphisms = 6 (D3) | chromatic_number = 3 | chromatic_index = 3 | diameter = 1 | radius = 1 | girth = 3 | notation = C_3 or K_3 | properties = 2-regular Vertex-transitive Edge-transitive Unit distance Hamiltonian Eulerian
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 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 (x-2)(x-1)x.
References
References
- "Triangle Graph".
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