首页/论文/2012.13898

arXiv 2012.138982020-12-27math.CO

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

Ravil Bildanov, Viktor Panshin, Grigory Ryabov

备注：: 21 pages
DOI：: 10.1007/s00373-021-02364-z(0123456789().,-vol(V0)123456789().,-volV)

英文摘要：

The WL-rank of a digraph $Γ$ is defined to be the rank of the coherent configuration of $Γ$. The WL-dimension of $Γ$ is defined to be the smallest positive integer $m$ for which $Γ$ 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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