{"month":"06","date_published":"2024-06-19T00:00:00Z","citation":{"chicago":"Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined by Their Spectrum.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/qmath/haae030\">https://doi.org/10.1093/qmath/haae030</a>.","ama":"Koval I, Kwan MA. Exponentially many graphs are determined by their spectrum. <i>Quarterly Journal of Mathematics</i>. 2024;75(3):869-899. doi:<a href=\"https://doi.org/10.1093/qmath/haae030\">10.1093/qmath/haae030</a>","short":"I. Koval, M.A. Kwan, Quarterly Journal of Mathematics 75 (2024) 869–899.","ista":"Koval I, Kwan MA. 2024. Exponentially many graphs are determined by their spectrum. Quarterly Journal of Mathematics. 75(3), 869–899.","mla":"Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined by Their Spectrum.” <i>Quarterly Journal of Mathematics</i>, vol. 75, no. 3, Oxford University Press, 2024, pp. 869–99, doi:<a href=\"https://doi.org/10.1093/qmath/haae030\">10.1093/qmath/haae030</a>.","ieee":"I. Koval and M. A. Kwan, “Exponentially many graphs are determined by their spectrum,” <i>Quarterly Journal of Mathematics</i>, vol. 75, no. 3. Oxford University Press, pp. 869–899, 2024.","apa":"Koval, I., &#38; Kwan, M. A. (2024). Exponentially many graphs are determined by their spectrum. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haae030\">https://doi.org/10.1093/qmath/haae030</a>"},"article_processing_charge":"Yes (via OA deal)","file":[{"file_size":946411,"access_level":"open_access","date_updated":"2024-09-06T12:23:57Z","success":1,"relation":"main_file","creator":"cchlebak","date_created":"2024-09-06T12:23:57Z","file_name":"2024_QuJofMath_Koval.pdf","checksum":"abf200d37ad69e6f2c0750a30296ad97","content_type":"application/pdf","file_id":"17851"}],"language":[{"iso":"eng"}],"year":"2024","publisher":"Oxford University Press","acknowledgement":"Matthew Kwan was supported by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777.","department":[{"_id":"MaKw"},{"_id":"VaKa"}],"corr_author":"1","abstract":[{"lang":"eng","text":"As a discrete analogue of Kac’s celebrated question on ‘hearing the shape of a drum’ and towards a practical\r\ngraph isomorphism test, it is of interest to understand which graphs are determined up to isomorphism by\r\ntheir spectrum (of their adjacency matrix). A striking conjecture in this area, due to van Dam and Haemers,\r\nis that ‘almost all graphs are determined by their spectrum’, meaning that the fraction of unlabelled n-vertex\r\ngraphs which are determined by their spectrum converges to 1 as n → ∞.\r\nIn this paper, we make a step towards this conjecture, showing that there are exponentially many n-vertex\r\ngraphs which are determined by their spectrum. This improves on previous bounds (of shape e\r\nc\r\n√\r\nn\r\n). We also\r\npropose a number of further directions of research.\r\n"}],"oa_version":"Published Version","type":"journal_article","file_date_updated":"2024-09-06T12:23:57Z","external_id":{"arxiv":["2309.09788"]},"page":"869-899","date_created":"2024-09-01T22:01:07Z","license":"https://creativecommons.org/licenses/by/4.0/","oa":1,"status":"public","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"author":[{"first_name":"Illya","full_name":"Koval, Illya","last_name":"Koval","id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","full_name":"Kwan, Matthew Alan"}],"publication_status":"published","has_accepted_license":"1","_id":"17475","project":[{"name":"Randomness and structure in combinatorics","grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"scopus_import":"1","article_type":"original","issue":"3","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"volume":75,"intvolume":"        75","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","ddc":["500"],"title":"Exponentially many graphs are determined by their spectrum","quality_controlled":"1","doi":"10.1093/qmath/haae030","publication":"Quarterly Journal of Mathematics","day":"19","date_updated":"2024-09-06T12:39:16Z"}