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windmill graph
In the mathematical field of graph theory, the windmill graph Wd(''k'',''n'') is an undirected graph constructed for ''k'' ≥ 2 and ''n'' ≥ 2 by joining ''n'' copies of the complete graph ''Kk'' at a shared vertex. That is, it is a 1-clique-sum of these complete graphs.〔Gallian, J. A. "Dynamic Survey DS6: Graph Labeling." Electronic J. Combinatorics, DS6, 1-58, Jan. 3, 2007. ().〕
==Properties==
It has ''(k-1)n+1'' vertices and ''nk(k−1)/2'' edges, girth 3 (if ''k > 2''), radius 1 and diameter 2.
It has vertex connectivity 1 because its central vertex is an articulation point; however, like the complete graphs from which it is formed, it is ''(k-1)''-edge-connected. It is trivially perfect and a block graph.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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