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In graph theory, the tensor product ''G'' × ''H'' of graphs ''G'' and ''H'' is a graph such that * the vertex set of ''G'' × ''H'' is the Cartesian product ''V(G)'' × ''V(H)''; and * any two vertices ''(u,u')'' and ''(v,v')'' are adjacent in ''G'' × ''H'' if and only if * *''u' '' is adjacent with ''v' '' and * *''u'' is adjacent with ''v''. The tensor product is also called the direct product, categorical product, cardinal product, relational product, Kronecker product, weak direct product, or conjunction. As an operation on binary relations, the tensor product was introduced by Alfred North Whitehead and Bertrand Russell in their Principia Mathematica (). It is also equivalent to the Kronecker product of the adjacency matrices of the graphs. The notation ''G'' × ''H'' is also sometimes used to represent another construction known as the Cartesian product of graphs, but more commonly refers to the tensor product. The cross symbol shows visually the two edges resulting from the tensor product of two edges. ==Examples== * The tensor product ''G'' × ''K''2 is a bipartite graph, called the bipartite double cover of ''G''. The bipartite double cover of the Petersen graph is the Desargues graph: ''K''2 × ''G''(5,2) = ''G''(10,3). The bipartite double cover of a complete graph ''Kn'' is a crown graph (a complete bipartite graph ''K''''n'',''n'' minus a perfect matching). * The tensor product of a complete graph with itself is the complement of a Rook's graph. Its vertices can be placed in an ''n'' by ''n'' grid, so that each vertex is adjacent to the vertices that are not in the same row or column of the grid. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tensor product of graphs」の詳細全文を読む スポンサード リンク
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