The FriendshipGraph(m) function creates the friendship graph on 2m+1 vertices.

It is formed by joining m copies of the cycle graph on 3 elements together at a single common vertex.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$F≔\mathrm{FriendshipGraph}\left(3\right)$

$F≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 7\; vertices\; and\; 9\; edge(s)}$

$\mathrm{Girth}\left(F\right)$

$3$

$\mathrm{ChromaticIndex}\left(F\right)$

$6$

$\mathrm{DrawGraph}\left(F\right)$

"Friendship graph", Wikipedia. http://en.wikipedia.org/wiki/Friendship_graph

Erdős, Paul; Rényi, Alfréd; Sós, Vera T. (1966), "On a problem of graph theory", Studia Sci. Math. Hungar., 1: 215–235.

The GraphTheory[SpecialGraphs][FriendshipGraph] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.