Friendship graph

Friendship graph
The friendship graph F8.
Vertices	2n + 1
Edges	3n
Radius	1
Diameter	2
Girth	3
Chromatic number	3
Chromatic index	2n
Properties	Unit distance Planar Eulerian Factor-critical Locally linear
Notation	Fn
Table of graphs and parameters

In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) F_n is a planar, undirected graph with 2n + 1 vertices and 3n edges.^[1]

The friendship graph F_n 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 F_n 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.