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On the WL-dimension of circulant graphs of prime power order
Ilia Ponomarenko · 2022-06-30 · via math.CO updates on arXiv.org

The WL-dimension of a graph X is the smallest positive integer m such that the m-dimensional Weisfeiler-Leman algorithm correctly tests the isomorphism between X and any other graph. It is proved that the WL-dimension of any circulant graph of prime power order is at most 3, and this bound cannot be reduced. The proof is based on using theories of coherent configurations and Cayley schemes over a cyclic group.

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