| Friendship graph | |
|---|---|
 The friendship graph F8. | |
| Vertices | 2n + 1 |
| Edges | 3n |
| Radius | 1 |
| Diameter | 2 |
| Girth | 3 |
| Chromatic number | 3 |
| Chromatic index | 2n |
| Properties | |
| Notation | Fn |
| Table of graphs and parameters | |
In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and 3n edges.[1]
The friendship graph Fn can be constructed by joining n copies of the cycle graph C3 with a common vertex, which becomes a universal vertex for the graph.[2]
By construction, the friendship graph Fn is isomorphic to the windmill graph Wd(3, n). It is unit distance with girth 3, diameter 2 and radius 1. The graph F2 is isomorphic to the butterfly graph. Friendship graphs are generalized by the triangular cactus graphs.
- ^ Weisstein, Eric W., "Dutch Windmill Graph", MathWorld
- ^ Gallian, Joseph A. (January 3, 2007), "A dynamic survey of graph labeling", Electronic Journal of Combinatorics: DS6, doi:10.37236/27.