The k-dimensional Weisfeiler-Leman algorithm ($k\text{-}\mathrm{WL}$) is a fruitful approach to the Graph Isomorphism problem. $2\text{-}\mathrm{WL}$ corresponds to the original algorithm suggested by Weisfeiler and Leman over 50 years ago. $1\text{-}\mathrm{WL}$ is the classical color refinement routine. Indistinguishability by $k\text{-}\mathrm{WL}$ is an equivalence relation on graphs that is of fundamental importance for isomorphism testing, descriptive complexity theory, and graph similarity testing which is also of some relevance in artificial intelligence. Focusing on dimensions $k=1,2$, we investigate subgraph patterns whose counts are $k\text{-}\mathrm{WL}$ invariant, and whose occurrence is $k\text{-}\mathrm{WL}$ invariant. We achieve a complete description of all such patterns for dimension $k=1$ and considerably extend the previous results known for $k=2$.

所述ķ维Weisfeiler-莱曼算法（$ķ\text{--}\mathrm{WL}$）是解决图同构问题的有效方法。 $2\text{--}\mathrm{WL}$ 对应于Weisfeiler和Leman在50年前提出的原始算法。 $\mathrm{1个}\text{--}\mathrm{WL}$是经典的色彩优化程序。不可分辨性$ķ\text{--}\mathrm{WL}$是图上的等价关系，这对于同构测试，描述性复杂性理论和图相似性测试（在人工智能中也有一定意义）至关重要。专注于尺寸$ķ=\mathrm{1个}，2$，我们调查计数为 $ķ\text{--}\mathrm{WL}$ 不变的，其出现是 $ķ\text{--}\mathrm{WL}$不变的 我们获得了所有此类尺寸模式的完整描述$ķ=\mathrm{1个}$ 并大大扩展了先前已知的结果 $ķ=2$。