## 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.

Original language | English |
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Pages (from-to) | 87-115 |

Number of pages | 29 |

Journal | Discrete Mathematics |

Volume | 255 |

Issue number | 1-3 |

DOIs | |

State | Published - 28 Aug 2002 |

## Keywords

- Coherent algebra
- Computer enumeration
- Directed strongly regular graph
- Transitive permutation group

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics