Small vertex-transitive directed strongly regular graphs
A simple directed graph \(\Gamma\) is called directed strongly regular graph with parameters \((n,k,\mu,\lambda,t)\) if its adjacency matrix \(A=A(\Gamma)\) satisfies \(AJ=JA=kJ\) and \(A^2=tI+\lambda A+\mu(J-I-A)\). In this paper all such graphs with \(n\) vertices, \(n\leq 20\), having vertex-transitive automorphism group are determined with the aid of a computer. This, together with a recent result by Jorgensen gives a complete answer to Duval's question about the existence of directed strongly regular graphs with \(n\leq 20\).
scientific article; zbMATH DE number 1838884
scientific article