  We prove that the number of iterations taken by the Weisfeiler-Leman
algorithm for configurations coming from Schreier graphs is closely linked to
the diameter of the graphs themselves: an upper bound is found for general
Schreier graphs, and a lower bound holds for particular cases, such as for
Schreier graphs with $G=\mbox{SL}_{n}({\mathbb F}_{q})$ ($q>2$) acting on
$k$-tuples of vectors in ${\mathbb F}_{q}^{n}$; moreover, an exact expression
is found in the case of Cayley graphs.
