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bipartite half
In graph theory, the bipartite half of a bipartite graph ''G'' = (''U'',''V'',''E'') is a graph whose vertex set is one of the two sides of the bipartition (without loss of generality, ''U'') and in which there is an edge ''u''''i''''u''''j'' for each two vertices ''u''''i'' and ''u''''j'' in ''U'' that are at distance two from each other in ''G''.〔.〕 That is, in a more compact notation, the bipartite half is ''G''2() where the superscript 2 denotes the square of a graph and the square brackets denote an induced subgraph.
For instance, the bipartite half of the complete bipartite graph ''K''''n'',''n'' is the complete graph ''K''''n'' and the bipartite half of the hypercube graph is the halved cube graph.
When ''G'' is a distance-regular graph, its two bipartite halves are both distance-regular.〔.〕
==See also==
*Bipartite double cover
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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