A Schurian graph is a finite graph 
for which the coherent
configuration determined by the stable coloring produced by the two-dimensional
Weisfeiler-Leman algorithm is Schurian.
Equivalently, the color classes are exactly the orbits of the componentwise action
of the automorphism group 
on ordered pairs of vertices
(Li et al. 2026).
When the associated coherent configuration is homogeneous, it is a Schurian scheme. Li et al. (2026) proved that every Schurian polyhedral graph has Weisfeiler-Leman dimension at most 2 and conjectured that every polyhedral graph is Schurian.
