{"id":"https://openalex.org/W2053730492","doi":"https://doi.org/10.1016/s0012-365x(00)00172-2","title":"The integral sum number of complete bipartite graphs Kr,s","display_name":"The integral sum number of complete bipartite graphs Kr,s","publication_year":2001,"publication_date":"2001-08-01","ids":{"openalex":"https://openalex.org/W2053730492","doi":"https://doi.org/10.1016/s0012-365x(00)00172-2","mag":"2053730492"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(00)00172-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(00)00172-2","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109504216","display_name":"Wenjie He","orcid":null},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenjie He","raw_affiliation_strings":["Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064514754","display_name":"Yufa Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yufa Shen","raw_affiliation_strings":["Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100331160","display_name":"Lixin Wang","orcid":"https://orcid.org/0000-0002-9497-461X"},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lixin Wang","raw_affiliation_strings":["Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004840229","display_name":"Yanxun Chang","orcid":"https://orcid.org/0000-0001-7766-5084"},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanxun Chang","raw_affiliation_strings":["Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046573240","display_name":"Qingde Kang","orcid":null},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingde Kang","raw_affiliation_strings":["Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034738551","display_name":"Xinkai Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinkai Yu","raw_affiliation_strings":["Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of applied mathematics, Hebei University of Technology, Box 134, Tianjin 300130, People's Republic of China","institution_ids":["https://openalex.org/I184843921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5109504216"],"corresponding_institution_ids":["https://openalex.org/I184843921"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.17825911,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"239","issue":"1-3","first_page":"137","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9980999827384949,"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/T11797","display_name":"graph theory and CDMA systems","score":0.986299991607666,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9108257293701172},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.814413845539093},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6856901049613953},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5176416039466858},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.44907599687576294},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3094639480113983}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9108257293701172},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.814413845539093},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6856901049613953},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5176416039466858},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.44907599687576294},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3094639480113983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(00)00172-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(00)00172-2","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2586280130","https://openalex.org/W4221143622","https://openalex.org/W2089088747","https://openalex.org/W2091826982","https://openalex.org/W245205139","https://openalex.org/W2036057584","https://openalex.org/W4246000090","https://openalex.org/W2950502967","https://openalex.org/W1981723335","https://openalex.org/W4390409907"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}