{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-proof-system-for-graph-non-isomorphism","title":"A proof system for graph (non)-isomorphism verification","arxiv_id":"2112.14303","date":"2021-12-28","proceeding":null,"authors":["Milan Banković","Ivan Drecun","Filip Marić"],"abstract":"In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze a state-of-the-art algorithm for canonical labelling of graphs (described by McKay and Piperno) and formulate it in terms of a formal proof system. We provide an implementation that can export a proof that the obtained graph is the canonical form of a given graph. Such proofs are then verified by our independent checker and can be used to confirm that two given graphs are not isomorphic.","url_abs":"https://arxiv.org/abs/2112.14303v5","url_pdf":"https://arxiv.org/pdf/2112.14303v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-proof-system-for-graph-non-isomorphism","repo_url":"https://github.com/milanbankovic/isocert","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}