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A circulant graph is a Cayley graph of a finite cyclic group. The Weisfeiler-Leman-dimension of a circulant graph X with respect to the class of all circulant graphs is the smallest positive integer~m such that the m-dimensional Weisfeiler-Leman algorithm correctly tests the isomorphism between X and any other circulant graph. It is proved that for a circulant graph of order n this dimension is less than or equal to (n) +3, where (n) is the number of prime divisors of~n.
Wu et al. (Sat,) studied this question.