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In the mathematical field of graph theory, the friendship graph Fn is a planar, undirected graph with 2n + 1 vertices and 3n edges.
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.
By construction, the friendship graph Fn is isomorphic to the windmill graph Wd. It is unit distance with girth 3, diameter 2 and radius 1. The graph F2 is isomorphic to the butterfly graph.
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