Elsevier

Discrete Mathematics

Volume 255, Issues 1–3, 28 August 2002, Pages 87-115
Discrete Mathematics

Small vertex-transitive directed strongly regular graphs

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Abstract

We consider directed strongly regular graphs defined in 1988 by Duval. All such graphs with n vertices, n⩽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 presented. This, together with a recent result by Jørgensen, gives a complete answer on Duval's question about the existence of directed strongly regular graphs with n⩽20. The paper includes catalogues of all generated graphs and certain theoretical generalizations based on some known and new graphs.

Keywords

Directed strongly regular graph
Coherent algebra
Transitive permutation group
Computer enumeration

Cited by (0)

1

Partially supported by the research grant No. 6782-1-95 of the Israeli Ministry of Science.

2

Partially supported by the Israeli Ministry of Absorption, by the research grant No. 6782-1-95 of the Israeli Ministry of Science, and by the Department of Mathematics and Computer Science of the University of the South Pacific, Fiji Islands.