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crown graph
In graph theory, a branch of mathematics, a crown graph on 2''n'' vertices is an undirected graph with two sets of vertices ''u''''i'' and ''v''''i'' and with an edge from ''u''''i'' to ''v''''j'' whenever ''i'' ≠ ''j''. The crown graph can be viewed as a complete bipartite graph from which the edges of a perfect matching have been removed, as the bipartite double cover of a complete graph, as the tensor product ''K''''n'' × ''K''''2'', or as a bipartite Kneser graph ''H''''n'',1 representing the 1-item and (''n'' − 1)-item subsets of an ''n''-item set, with an edge between two subsets whenever one is contained in the other.
==Examples==
The 6-vertex crown graph forms a cycle, and the 8-vertex crown graph is isomorphic to the graph of a cube.
In the Schläfli double six, a configuration of 12 lines and 30 points in three-dimensional space, the twelve lines intersect each other in the pattern of a 12-vertex crown 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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