The graph isomorphism problem — determining whether two graphs are structurally identical — is one of the few natural problems in computational complexity whose status is genuinely uncertain. The Weisfeiler-Lehman (WL) hierarchy provides increasingly powerful tests: k-WL colors vertex tuples and iterates until stable. For most graphs, low-dimensional WL works. But strongly regular graphs are the hard cases — they are precisely the graphs designed to look identical under color refinement.
This paper introduces a destructive strategy. The DRESS fingerprint deletes one vertex at a time, computes a fingerprint of the resulting subgraph, then combines the distribution over all single-deletion subgraphs into a graph-level fingerprint. Applied to all 51,718 non-isomorphic strongly regular graphs across 16 parameter families, it achieves 100% separation.
The result breaks known algebraic boundaries: the Rook Lā(4) vs. Shrikhande pair, SRG(16,6,2,2), is provably indistinguishable by 3-WL. DRESS separates them. The mechanism is that vertex deletion breaks the automorphism group's uniform action — different vertices, when removed, produce structurally distinguishable residues. The symmetry that makes the whole graph hard to fingerprint does not survive the removal of a single vertex.
A destructive operation — removing structure — creates distinguishing power that exceeds what constructive methods (adding color dimensions) achieve. Less graph produces more information.