On the Weisfeiler–Leman dimension of circulant graphs

A circulant graph is the 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 properly tests 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 $\Omega(n)+3$, where $\Omega(n)$ is the total number of prime divisors of $n$.