Rank of adjacency matrices of directed (strongly) regular graphs Original Research Article

For a positive integer r we consider the set Br of all values of image 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 Br 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 image. We use this to exclude existence of directed strongly regular graphs for infinitely many feasible parameter sets.