Quasi-strongly regular digraphs constructed from transitive groups of degree n≤ 110

@misc{crnkovic2026quasistrongly,
  title = {{Quasi-strongly regular digraphs constructed from transitive groups of degree $n\leq 110$}},
  author = {Vedrana Mikulić Crnković and Matea Zubović Žutolija},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10075},
  eprint = {2609.10075},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10075},
}

TY  - UNPB
TI  - Quasi-strongly regular digraphs constructed from transitive groups of degree n≤ 110
AU  - Vedrana Mikulić Crnković
AU  - Matea Zubović Žutolija
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10075
UR  - https://arxiv.org/abs/2609.10075
AB  - In this paper we present a method for constructing directed regular graphs from a transitive permutation group. This method is a generalization of a construction method for transitive 1-designs from a finite group, described in \cite{dean1}. Using this construction, we prove the existence of directed strongly regular graphs with parameters $(72,25,15,6,10)$, $(96,11,4,3,1)$, $(96,22,16,8,4)$, $(96,26,11,7,7)$, $(96,29,23,10,8)$, $(96,42,32,16,20)$, $(96,45,35,22,20)$ and $(165,60,36,23,21)$. Finally, we classify quasi-strongly regular digraphs arising from transitive permutation groups of degree at most $30$ and from primitive permutation groups of degrees from $31$ to $110$ and rank at most $30$.
ER  -