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arXiv · 2312.00460

A large family of strongly regular graphs with small Weisfeiler-Leman dimension

Jinzhuan Cai·Jin Guo·Alexander L. Gavrilyuk·Ilia Ponomarenko
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Abstract

In 2002, D. Fon-Der-Flaass constructed a prolific family of strongly regular graphs. In this paper, we prove that for infinitely many natural numbers $n$, this family contains $n^{Ω(n^{2/3})}$ strongly regular $n$-vertex graphs $X$ with the same parameters, which satisfy the following condition: an isomorphism between $X$ and any other graph can be verified by the $4$-dimensional Weisfeiler-Leman algorithm.

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Jinzhuan Cai, Jin Guo, Alexander L. Gavrilyuk, Ilia Ponomarenko. 2023-12-01. A large family of strongly regular graphs with small Weisfeiler-Leman dimension. https://arxiv.org/abs/2312.00460

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