Non-existence of directed strongly regular graphs

Representations of directed strongly regular graphs

We develop a theory of representations in Rm for directed strongly regular graphs, which gives a new proof of a nonexistence condition of Jørgensen [8]. We also describe some new constructions.

Small vertex-transitive directed strongly regular graphs

We consider directed strongly regular graphs de2ned in 1988 by Duval. All such graphs with n vertices, n6 20, having a vertex-transitive automorphism group, are determined with the aid of a computer. As a consequence, we prove the existence of directed strongly regular graphs for three feasible parameter sets listed by Duval. For one parameter set a computer-free proof of the nonexistence is pr...

Directed Strongly Regular Graphs and Their Codes

Directed Strongly Regular Graphs (DSRG) were introduced by Duval as a generalization of strongly regular graphs (SRG’s) [4]. As observed in [8] a special case of these are the doubly regular tournaments or equivalently, the skew Hadamard matrices. As the latter already lead to many interesting codes [10] it is natural to consider the more general case of codes constructed from the adjacency mat...

New mixed Moore graphs and directed strongly regular graphs

A directed strongly regular graph with parameters (n, k, t, λ, μ) is a k-regular directed graph with n vertices satisfying that the number of walks of length 2 from a vertex x to a vertex y is t if x = y, λ if there is an edge directed from x to y and μ otherwise. If λ = 0 and μ = 1 then we say that it is a mixed Moore graph. It is known that there are unique mixed Moore graphs with parameters ...

Strongly regular graphs with non-trivial automorphisms