  We describe a method for generating graphs that provide difficult examples
for practical Graph Isomorphism testers. We first give the theoretical
construction, showing that we can have a family of graphs without any
non-trivial automorphisms which also have high Weisfeiler-Leman dimension. The
construction is based on properties of random 3XOR-formulas. We describe how to
convert such a formula into a graph which has the desired properties with high
probability. We validate the method by an experimental implementation. We
construct random formulas and validate them with a SAT solver to filter through
suitable ones, and then convert them into graphs. Experimental results
demonstrate that the resulting graphs do provide hard examples that match the
hardest known benchmarks for graph isomorphism.
