{"id":"https://openalex.org/W1908345864","doi":"https://doi.org/10.37236/397","title":"On the Koolen–Park inequality and Terwilliger graphs","display_name":"On the Koolen–Park inequality and Terwilliger graphs","publication_year":2010,"publication_date":"2010-09-13","ids":{"openalex":"https://openalex.org/W1908345864","doi":"https://doi.org/10.37236/397","mag":"1908345864"},"language":"en","primary_location":{"id":"doi:10.37236/397","is_oa":true,"landing_page_url":"https://doi.org/10.37236/397","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r125/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/v17i1r125/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056670846","display_name":"Alexander L. Gavrilyuk","orcid":"https://orcid.org/0000-0001-9296-0313"},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I4210105350","display_name":"N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/029fhmb28","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210105350","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Alexander L. Gavrilyuk","raw_affiliation_strings":["Department of Algebra and Topology Institute of Mathematics and Mechanics Ural Division of the Russian Academy of Sciences, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Algebra and Topology Institute of Mathematics and Mechanics Ural Division of the Russian Academy of Sciences, Russia","institution_ids":["https://openalex.org/I4210105350","https://openalex.org/I1313323035"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056670846"],"corresponding_institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I4210105350"],"apc_list":null,"apc_paid":null,"fwci":0.9622,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.68123667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9955000281333923,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.809046745300293},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7279824018478394},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.643162727355957},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41008543968200684},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3899586796760559},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.03936266899108887}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.809046745300293},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7279824018478394},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.643162727355957},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41008543968200684},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3899586796760559},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.03936266899108887}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/397","is_oa":true,"landing_page_url":"https://doi.org/10.37236/397","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r125/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:10.37236/397","is_oa":true,"landing_page_url":"https://doi.org/10.37236/397","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r125/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":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/1","display_name":"No poverty"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1908345864.pdf","grobid_xml":"https://content.openalex.org/works/W1908345864.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1976243638","https://openalex.org/W2138033161","https://openalex.org/W4298236575"],"related_works":["https://openalex.org/W2374829073","https://openalex.org/W2385671392","https://openalex.org/W2610737932","https://openalex.org/W2741785956","https://openalex.org/W2134745787","https://openalex.org/W2383129606","https://openalex.org/W2042289434","https://openalex.org/W2393028428","https://openalex.org/W2736557199","https://openalex.org/W2952342369"],"abstract_inverted_index":{"J.H.":[0],"Koolen":[1],"and":[2,56],"J.":[3],"Park":[4],"proved":[5],"a":[6,15,23,35],"lower":[7],"bound":[8],"for":[9,26],"the":[10,43,45,49],"intersection":[11],"number":[12],"$c_2$":[13],"of":[14],"distance-regular":[16],"graph":[17,24,47,51],"$\\Gamma$.":[18],"Moreover,":[19],"they":[20],"showed":[21],"that":[22,40],"$\\Gamma$,":[25],"which":[27],"equality":[28,53],"is":[29,34,42,54],"attained":[30,55],"in":[31],"this":[32],"bound,":[33],"Terwilliger":[36],"graph.":[37],"We":[38],"prove":[39],"$\\Gamma$":[41],"icosahedron,":[44],"Doro":[46],"or":[48],"Conway\u2013Smith":[50],"if":[52],"$c_2\\ge":[57],"2$.":[58]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T20:47:17.329874","created_date":"2025-10-10T00:00:00"}