Skip to content
DraconiticResearch
Search Sources API
206,690 studies31 sourcesUpdated 22 min ago
PreprintCC BY 4.0arXiv

An infinite family of intransitive directed strongly regular graphs with rank 6 Weisfeiler--Leman closure

  • Štefan Gyürki
Open at sourcePDFDOICite

Abstract

We construct an infinite family of directed strongly regular graphs (DSRGs) with intransitive full automorphism groups whose Weisfeiler--Leman closure are association schemes of rank 6. This is the smallest possible rank for an association scheme admitting a proper DSRG merging. We also exhibit rigid sporadic DSRGs with the same closure property, showing that combinatorial regularity, group-theoretic symmetry, and Weisfeiler--Leman regularity capture fundamentally different aspects of graph structure.

Related

  1. Enumeration of small vertex-transitive directed strongly regular graphs
    A. E. Brouwer, Š. Gyürki
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Infinite series of Deza graphs with strongly regular children
    Mikhail P. Golubyatnikov
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  3. Infinite-variation Lévy processes are either strongly eroded or abrupt
    Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
    arXivPreprintCC BY-SA 4.0Full textProbabilityarXiv
  4. Coherent configuration on 3-uniform hypergraph over strongly regular graph
    Fajri Maulana
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. Complex Hadamard matrices and strongly regular graphs
    Ada Chan
    Discrete MathematicsPeer-reviewedCC BY-NC-ND7 citedCombinatorics & discrete mathematicsOpenAlex

Cite

BibTeXRIS
BibTeX
@misc{gyurki2026infinite,
  title = {{An infinite family of intransitive directed strongly regular graphs with rank 6 Weisfeiler--Leman closure}},
  author = {Štefan Gyürki},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25282},
  eprint = {2609.25282},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25282},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An infinite family of intransitive directed strongly regular graphs with rank 6 Weisfeiler--Leman closure
AU  - Štefan Gyürki
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25282
UR  - https://arxiv.org/abs/2609.25282
AB  - We construct an infinite family of directed strongly regular graphs (DSRGs) with intransitive full automorphism groups whose Weisfeiler--Leman closure are association schemes of rank 6. This is the smallest possible rank for an association scheme admitting a proper DSRG merging. We also exhibit rigid sporadic DSRGs with the same closure property, showing that combinatorial regularity, group-theoretic symmetry, and Weisfeiler--Leman regularity capture fundamentally different aspects of graph structure.
ER  -