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arXiv · 2012.13898

On WL-rank and WL-dimension of some Deza circulant graphs

Ravil Bildanov·Viktor Panshin·Grigory Ryabov
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Abstract

The WL-rank of a digraph $\Gamma$ 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 classify the Deza circulant graphs of WL-rank $4$. In additional, it is proved that each of these graphs has WL-dimension at most $3$. Finally, we establish that some families of Deza circulant graphs have WL-rank $5$ or $6$ and WL-dimension at most $3$.

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Ravil Bildanov, Viktor Panshin, Grigory Ryabov. 2020-12-27. On WL-rank and WL-dimension of some Deza circulant graphs. https://doi.org/10.1007/s00373-021-02364-z(0123456789().,-vol(v0)123456789().,-volv)

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