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Dutch Windmill Graph

DutchWindmillGraph

The Dutch windmill graph D_3^((m)), also called a friendship graph, is the graph obtained by taking m copies of the cycle graph C_3 with a vertex in common (Gallian 2007), and therefore corresponds to the usual windmill graph W_3^((m)). It is therefore natural to extend the definition to D_n^((m)), consisting of m copies of the cycle graph C_n.

By construction, the Dutch windmill graph D_n^((m)) has anarboricity m.

Precomputed properties of Dutch windmill graphs are implemented in the Wolfram Language as GraphData[{"DutchWindmill", {m, n}}].

Jiang and Shao (2026) proved that the Ramsey number R(D_3^((3)),D_3^((4)))=17. They denote D_3^((m)) by F_m and call it a fan, meaning m triangles with a single common vertex; this differs from the fan graph defined as the graph join of a singleton graph and a path graph. Jiang and Shao (2026) report Codex assistance with implementing, testing, and checking their programs.

See also

Windmill Graph

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References

Bondy, J. A. and Murty, U. S. R. Graph Theory. Berlin, Germany: Springer-Verlag, p. 81, 2008.Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin., Dynamic Survey DS6, Oct. 30, 2025. https://doi.org/10.37236/27.House of Graphs. Dutch Windmill Graphs. Butterfly Graph, Two 4-Cycles with Common Vertex, Friendship Graph F3, Mitsubishi Graph, and Friendship Graph F4.Jiang, H. and Shao, Z. "An 8+9 Gluing Computation for the Ramsey Number R(F_3,F_4)." 19 Oct 2026. https://arxiv.org/abs/2610.26109.

Referenced on Wolfram|Alpha

Dutch Windmill Graph

Cite this as:

Weisstein, Eric W. "Dutch Windmill Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DutchWindmillGraph.html

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