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Friendship graph
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<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> field of <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, the friendship graph (or Dutch windmill graph or n-fan) Fn is a <a href="/facts/Planar_graph/plREagr9">planar</a>, <a href="/facts/Undirected_graph/kw3eIBUe">undirected graph</a> with 2<i>n</i> + 1 <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">vertices</a> and 3<i>n</i> edges. </p><p>The friendship graph Fn can be constructed by joining n copies of the <a href="/facts/Cycle_graph/bYhnPDHc">cycle graph</a> <i>C</i>3 with a common vertex, which becomes a <a href="/facts/Universal_vertex/5YRHn7Y2">universal vertex</a> for the graph. </p><p>By construction, the friendship graph Fn is <a href="/facts/Graph_isomorphism/SBjVIhwW">isomorphic</a> to the <a href="/facts/Windmill_graph/83cRPHsu">windmill graph</a> Wd(3, <i>n</i>). It is <a href="/facts/Unit_distance_graph/8y4Ctq53">unit distance</a> with <a href="/facts/Girth_(graph_theory)/rPwRGgxj">girth</a> 3, diameter 2 and radius 1. The graph <i>F</i>2 is isomorphic to the <a href="/facts/Butterfly_graph/qWSnVrD6">butterfly graph</a>. Friendship graphs are generalized by the <a href="/facts/Triangular_cactus_graph/s85ekIxz">triangular cactus graphs</a>. </p>