{"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/using-symbolic-computation-to-prove","title":"Using symbolic computation to prove nonexistence of distance-regular graphs","arxiv_id":"1803.10797","date":"2018-03-28","proceeding":null,"authors":["Janoš Vidali"],"abstract":"A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array $\\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1), 4r(2r+1)(4t-1)\\}$ ($r, t \\ge 1$), $\\{135, 128, 16; 1, 16, 120\\}$, $\\{234, 165, 12; 1, 30, 198\\}$ or $\\{55, 54, 50, 35, 10; 1, 5, 20, 45, 55\\}$. In all cases, the proofs rely on equality in the Krein condition, from which triple intersection numbers are determined. Further combinatorial arguments are then used to derive nonexistence.","url_abs":"http://arxiv.org/abs/1803.10797v1","url_pdf":"http://arxiv.org/pdf/1803.10797v1.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":"using-symbolic-computation-to-prove","repo_url":"https://github.com/jaanos/sage-drg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"using-symbolic-computation-to-prove","repo_url":"https://github.com/jaanos/jaanos.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}