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arXiv · 2406.15822

On the Weisfeiler-Leman dimension of circulant graphs

Yulai Wu·Ilia Ponomarenko
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Abstract

A circulant graph is a Cayley graph of a finite cyclic group. The Weisfeiler-Leman-dimension of a circulant graph $X$ with respect to the class of all circulant graphs is the smallest positive integer~$m$ such that the $m$-dimensional Weisfeiler-Leman algorithm correctly tests the isomorphism between $X$ and any other circulant graph. It is proved that for a circulant graph of order $n$ this dimension is less than or equal to $Ω(n)+3$, where $Ω(n)$ is the number of prime divisors of~$n$.

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Yulai Wu, Ilia Ponomarenko. 2024-09-29. On the Weisfeiler-Leman dimension of circulant graphs. https://arxiv.org/abs/2406.15822

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