Directed Strongly Regular Graphs With Adjacency Matrix Of Rank 6

In this paper, we study 24 possibilities of directed strongly regular graphs with adjacency matrix of rank 6, our proof is based on an enumeration of 6x6 matrices with entries in {0,1}. At last, we get 4 families of directed strongly regular graphs with realizable parameter sets and adjacency matrix of rank 6, exclude 20 families of directed strongly regular graphs with feasible parameter sets and adjacency matrix of rank 6; partially solve the classification problem of directed strongly regular graphs with adjacency matrix of rank 6.