Friendship graph

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 $2 n + 1$ vertices and $3 n$ edges.

The friendship graph $F n$ can be constructed by joining $n$ copies of the cycle graph $C 3$ with a common vertex, which becomes a universal vertex for the graph.

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 $F 2$ is isomorphic to the butterfly graph. Friendship graphs are generalized by the triangular cactus graphs.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.