For a positive integer r we consider the set B-r of all values of k for which there exists an n x n matrix with entries 0 and 1 such that each row and each column has exactly k 1's and the matrix has rank r. We prove that the set B-r is finite, for every r.If there exists a k-regular directed graph on n vertices such that its adjacency matrix has rank r then k epsilon B-r. We use this to exclude existence of directed strongly regular graphs for infinitely many feasible parameter sets. (c) 2005 Elsevier Inc. All rights reserved.
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机译：对于正整数r，我们考虑所有k / n值的集合B-r，对于该值存在一个n x n矩阵，其矩阵项为0和1，使得每一行和每一列都恰好具有k 1，矩阵的秩为r。我们证明对于每个r集合B-r是有限的。如果在n个顶点上存在k正则有向图，使得其邻接矩阵的秩为r，则k / n epsilon B-r。我们使用它来排除存在无穷多个可行参数集的有向强正则图的存在。 （c）2005 Elsevier Inc.保留所有权利。
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