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,
a finite graph is Schurian when these color classes
are exactly the orbitals of the componentwise group
action of the automorphism group 
on ordered
pairs of vertices (Li et al. 2026).
A stable coloring is one that color refinement does not split further. When the associated coherent configuration is a homogeneous coherent configuration, 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.
Reh (2026) reported an exhaustive computer verification that all 413024847068 polyhedral graphs with at most 16 vertices are Schurian. This verifies a finite range of the conjecture, not the unrestricted assertion. Reh (2026) states that Claude assisted with implementation, verification design, and drafting.
