High Quality Content by WIKIPEDIA articles! In the mathematical field of graph theory, the windmill graph Wd(k,n) is a simple undirected graph with (k-1)n+1 vertices and nk(k?1)/2 edges. It is defined for k ? 2 and n ? 2. The windmill graph Wd(k,n) can be constructed by joining n copies of the complete graph Kk with a common vertex. It has girth 3 (if k > 2), radius 1 and diameter 2. By removing the central vertex of the windmill graph, it can be proved that it is a 1-vertex-connected graph. Each copy of the complete graph Kk is (k-1)-edge-connected graph. Therefore, the windmill graph is (k-1)-edge-connected. By construction, the windmill graph Wd(3,n) is the friendship graph Fn, the windmill graph Wd(2,n) is the star graph Sn and the windmill graph Wd(3,2) is the butterfly graph.

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