Rank of adjacency matrices of directed (strongly) regular graphs
Rank of adjacency matrices of directed (strongly) regular graphs
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DOI：
10.1016/j.laa.2005.05.005
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发表时间：
2005-09
影响因子：
1.1
通讯作者：
L. K. Jørgensen
中科院分区：
文献类型：
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作者：
L. K. Jørgensen
对于正整数r，我们考虑kn的所有值的集合Br.如果存在一个n×n矩阵，其项为0和1，使得每一行和每一列恰好有k个1‘S，且矩阵的秩为r.我们证明了，对于任意的r，集合Br2是有限的.如果存在n个顶点上的k-正则有向图，使得它的邻接矩阵有秩r，则kn∈bR.我们用它来排除无穷多个可行参数集的有向强正则图的存在性。
For a positive integer r we consider the set Brof all values of kn for which there exists an n×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 Bris finite, for every r. If there exists a k-regular directed graph on n vertices such that its adjacency matrix has rank r then kn∈Br. We use this to exclude existence of directed strongly regular graphs for infinitely many feasible parameter sets.