The -windmill graph is the graph obtained by taking copies of the complete graph with a vertex in common (Gallian 2011, p. 16). The -windmill graph is therefore isomorphic to the graph join .
The -windmill graph is isomorphic to the graph contraction and the -windmill graph is isomorphic to the -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].