Non-existence of directed strongly regular graphs Original Research Article

Directed strongly regular graphs were introduced by Duval in 1988. We give several non-existence results, each excluding infinite series of feasible parameter sets: We prove a result that extends the absolute bound for strongly regular graphs, and we give a characterization of directed strongly regular graphs whose adjacency matrix has rank 3 or 4. We also give some combinatorial non-existence results and a construction of five new directed strongly regular graphs.