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.

中文翻译：

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一些Deza循环图的WL-Rank和WL-Dimension

在WL-秩一有向图的\（\伽玛\）被定义为的相干结构的秩\（\伽玛\） 。在WL-尺寸的\（\伽玛\）被定义为最小的正整数 米为哪些\（\伽玛\）是由所标识的米维Weisfeiler-莱曼算法。我们对 WL-rank 4 的 Deza 循环图进行分类。此外，证明了这些图中的每一个都具有最多 3 的 WL-维数。最后，我们建立了一些 Deza 循环图族具有 WL-rank 5 或 6 和WL-维度至多3。