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Determinants, Permanents, and Bipartite Graphs

Frank HararyRand Corporation

出版	Rand Corporation, 1968
URL	http://books.google.com.hk/books?id=_rMKGQAACAAJ&hl=&source=gbs_api

註釋

The combinatorial properties of a nonnegative matrix M are captured by that binary matrix A = A(M) in which the entries are 1 whenever those of M are positive. If A is a square matrix, then it can be regarded as the adjacency matrix of a directed graph (digraph). If A is rectangular, a bipartite graph (bigraph) can be associated with A; of course this can also be done for A square. The determinant of the adjacency matrix of a graph or digraph has been expressed in terms of its structure, and so has the permanent. The purposes of this report are to express the permanent of a square or rectangular binary matrix in terms of the associated bigraph, and to formulate the determinant of a square matrix in terms of its bigraph. (Author).