Windmill Graph


The (m,n)-windmill graph is the graph obtained by taking m copies of the complete graph K_n with a vertex in common (Gallian 2011, p. 16). The (m,n)-windmill graph is therefore isomorphic to the graph join mK_(n-1)+K_1.

The (2,n)-windmill graph is isomorphic to the graph contraction K_n·K_n and the (m,3)-windmill graph is isomorphic to the (m,3)-Dutch windmill graph.

Special cases are summarized in the following table.

Windmill graphs are geodetic.

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

See also

Double Cone Graph, Dutch Windmill Graph, Graph Join, Windmill

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Benson, M. and Lee, S. M. "On Cordialness of Regular Windmill Graphs." Congr. Numer. 68, 45-58, 1989.Bermond, J. C. "Graceful Graphs, Radio Antennae and French Windmills." Graph Theory and Combinatorics. London: Pitman, pp. 18-37, 1979.Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin. DS6. Dec. 21, 2018., K. M.; Rogers, D. G.; Teo, H. K.; and Yap, K. Y. "Graceful Graphs: Some Further Results and Problems." Congr. Numer. 29, 559-571, 1980.

Referenced on Wolfram|Alpha

Windmill Graph

Cite this as:

Weisstein, Eric W. "Windmill Graph." From MathWorld--A Wolfram Web Resource.

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