{"id":"https://openalex.org/W1574538617","doi":"https://doi.org/10.37236/263","title":"Sudoku Graphs are Integral","display_name":"Sudoku Graphs are Integral","publication_year":2009,"publication_date":"2009-07-24","ids":{"openalex":"https://openalex.org/W1574538617","doi":"https://doi.org/10.37236/263","mag":"1574538617"},"language":"en","primary_location":{"id":"doi:10.37236/263","is_oa":true,"landing_page_url":"https://doi.org/10.37236/263","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n25/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054381053","display_name":"Torsten Sander","orcid":null},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Torsten Sander","raw_affiliation_strings":["Institut fr Mathematik Technische Universitt Clausthal D-38678 Clausthal-Zellerfeld, Germany","Clausthal Univ. of Technol"],"affiliations":[{"raw_affiliation_string":"Institut fr Mathematik Technische Universitt Clausthal D-38678 Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]},{"raw_affiliation_string":"Clausthal Univ. of Technol","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054381053"],"corresponding_institution_ids":["https://openalex.org/I43980791"],"apc_list":null,"apc_paid":null,"fwci":2.9908,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.90750084,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9589999914169312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8968014717102051},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7038445472717285},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3920608460903168}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8968014717102051},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7038445472717285},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3920608460903168}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/263","is_oa":true,"landing_page_url":"https://doi.org/10.37236/263","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/263","is_oa":true,"landing_page_url":"https://doi.org/10.37236/263","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1n25/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1574538617.pdf","grobid_xml":"https://content.openalex.org/works/W1574538617.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1515707356","https://openalex.org/W1608618407","https://openalex.org/W1911731259","https://openalex.org/W1969129092","https://openalex.org/W1971162166","https://openalex.org/W1986862187","https://openalex.org/W2002896906","https://openalex.org/W2053934832","https://openalex.org/W2080681131","https://openalex.org/W2100215899","https://openalex.org/W2117060314","https://openalex.org/W2121376290","https://openalex.org/W2131353462","https://openalex.org/W2142437260","https://openalex.org/W2153116499","https://openalex.org/W2196559987","https://openalex.org/W2288891766","https://openalex.org/W2330548796","https://openalex.org/W2479778494"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Sudoku":[0],"graphs":[1],"have":[2],"only":[3],"5":[4],"or":[5],"6":[6],"distinct":[7],"eigenvalues":[8],"and":[9],"all":[10],"of":[11],"them":[12],"are":[13],"integers.":[14],"Moreover,":[15],"the":[16,24],"associated":[17],"eigenspaces":[18],"admit":[19],"bases":[20],"with":[21],"entries":[22],"from":[23],"set":[25],"$\\{0,":[26],"1,":[27],"-1\\}$.":[28]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}