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Minimum rank of a graph
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Minimum rank of a graph : ウィキペディア英語版
Minimum rank of a graph
In mathematics, the minimum rank is a graph parameter \operatorname(G) for any graph ''G''. It was motivated by the Colin de Verdière's invariant.
==Definition==
The adjacency matrix of a given undirected graph is a symmetric matrix whose rows and columns both correspond to the vertices of the graph. Its coefficients are all 0 or 1, and the coefficient in row ''i'' and column ''j'' is nonzero whenever vertex ''i'' is adjacent to vertex ''j'' in the graph. More generally, one can define a ''generalized adjacency matrix'' to be any matrix of real numbers with the same pattern of nonzeros. The minimum rank of the graph G is denoted by \operatorname (G) and is defined as the smallest rank of any generalized adjacency matrix of the 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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