Triangle graph
From HandWiki
| 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.[1]
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
References
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