The family of Weisfeiler–Leman equivalences on graphs is a widely studied
approximation of graph isomorphism with many different characterizations. We study
these and other approximations of isomorphism defined in terms of refinement
operators and Schurian polynomial approximation schemes (SPAS). The general
framework of SPAS allows us to study a number of parameters of the refinement
operators based on Weisfeiler–Leman refinement, logic with counting, lifts of
Weisfeiler–Leman as defined by Evdokimov and Ponomarenko, the invertible map
test introduced by Dawar and Holm, and variations of these, as well as to establish
relationships between them.
