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arXiv · 2609.25282

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

Štefan Gyürki
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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.

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Štefan Gyürki. 2026-09-21. An infinite family of intransitive directed strongly regular graphs with rank 6 Weisfeiler--Leman closure. https://arxiv.org/abs/2609.25282

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