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arXiv · 2109.15182

On WL-rank and WL-dimension of some Deza dihedrants

Grigory Ryabov·Leonid Shalaginov
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Abstract

The WL-rank of a graph $\Gamma$ is defined to be the rank of the coherent configuration of $\Gamma$. The WL-dimension of $\Gamma$ is defined to be the smallest positive integer $m$ for which $\Gamma$ is identified by the $m$-dimensional Weisfeiler-Leman algorithm. We establish that some families of strictly Deza dihedrants have WL-rank $4$ or $5$ and WL-dimension $2$. Computer calculations imply that every strictly Deza dihedrant with at most $59$ vertices is circulant or belongs to one of the above families. We also construct a new infinite family of strictly Deza dihedrants whose WL-rank is a linear function of the number of vertices.

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Grigory Ryabov, Leonid Shalaginov. 2021-09-30. On WL-rank and WL-dimension of some Deza dihedrants. https://arxiv.org/abs/2109.15182

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