A proof system for graph (non)-isomorphism verification

In order to be able to apply graph isomorphism checking within interactive theorem provers, either graph isomorphism checking algorithms must be mechanically verified, or their results must be verifiable by independent checkers. We analyze a state-of-the-art graph isomorphism checking algorithm (described by McKay and Piperno) and formulate it in a form of a formal proof system. We provide an implementation that can export a proof that an obtained graph is the canonical form of a given graph. Such proofs are then verified by our independent checker, and are used to certify that two given graphs are non-isomorphic.