{"id":"https://openalex.org/W3097675686","doi":"https://doi.org/10.1142/s0129626420400058","title":"The Connectivity of a Bipartite Graph and Its Bipartite Complementary Graph","display_name":"The Connectivity of a Bipartite Graph and Its Bipartite Complementary Graph","publication_year":2020,"publication_date":"2020-09-01","ids":{"openalex":"https://openalex.org/W3097675686","doi":"https://doi.org/10.1142/s0129626420400058","mag":"3097675686"},"language":"en","primary_location":{"id":"doi:10.1142/s0129626420400058","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626420400058","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","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/A5085199355","display_name":"Yingzhi Tian","orcid":"https://orcid.org/0000-0002-1595-9834"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yingzhi Tian","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-1595-9834","affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069077306","display_name":"Huaping Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huaping Ma","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034901505","display_name":"Liyun Wu","orcid":"https://orcid.org/0000-0001-7392-582X"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liyun Wu","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085199355"],"corresponding_institution_ids":["https://openalex.org/I96908189"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18063377,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"30","issue":"03","first_page":"2040005","last_page":"2040005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987999796867371,"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/T11476","display_name":"Graph theory and applications","score":0.9987999796867371,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/combinatorics","display_name":"Combinatorics","score":0.7667309045791626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.71985924243927},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6862809658050537},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5160322189331055},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.5116620063781738},{"id":"https://openalex.org/keywords/foster-graph","display_name":"Foster graph","score":0.4943256378173828},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4619823396205902},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.4530947804450989},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.43455737829208374},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3741095960140228}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7667309045791626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.71985924243927},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6862809658050537},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5160322189331055},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.5116620063781738},{"id":"https://openalex.org/C68996132","wikidata":"https://www.wikidata.org/wiki/Q3115485","display_name":"Foster graph","level":5,"score":0.4943256378173828},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4619823396205902},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.4530947804450989},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.43455737829208374},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3741095960140228}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129626420400058","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626420400058","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6000000238418579}],"awards":[{"id":"https://openalex.org/G1448350847","display_name":null,"funder_award_id":"11531011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8752940626","display_name":"k-\u70b9\u8fde\u901a\u56fe\u4e2d\u4fdd\u6301\u8fde\u901a\u5ea6\u7684\u5b50\u6811\u7684\u7814\u7a76","funder_award_id":"11861066","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2057250066","https://openalex.org/W2067217885","https://openalex.org/W2078743813","https://openalex.org/W2319043422","https://openalex.org/W2506153394","https://openalex.org/W4232896595"],"related_works":["https://openalex.org/W2107875203","https://openalex.org/W2380035736","https://openalex.org/W2394181405","https://openalex.org/W4362599212","https://openalex.org/W2022884461","https://openalex.org/W1568744482","https://openalex.org/W2382367825","https://openalex.org/W2081621039","https://openalex.org/W2013821601","https://openalex.org/W3159296125"],"abstract_inverted_index":{"In":[0,122],"1956,":[1],"Nordhaus":[2],"and":[3,7,13,23,53,114,118,136],"Gaddum":[4],"gave":[5],"lower":[6],"upper":[8],"bounds":[9],"on":[10,38],"the":[11,14,17,29,32,39,42,54,58,127],"sum":[12,40],"product":[15,43],"of":[16,20,28,31,44,63,133],"chromatic":[18],"number":[19],"a":[21,48,69,88,107],"graph":[22,49,90,102,109],"its":[24,99,137],"complement,":[25],"in":[26,47,57],"terms":[27],"order":[30],"graph.":[33],"Since":[34],"then,":[35],"any":[36],"bound":[37],"and/or":[41],"an":[45],"invariant":[46,56],"[Formula:":[50,60,64,91,103,111,115,119],"see":[51,61,65,92,97,104,112,116,120],"text]":[52,62,66,93,105,113,117],"same":[55],"complement":[59],"is":[67,106],"called":[68],"Nordhaus-Gaddum":[70,76,128],"type":[71,77,129],"inequality":[72],"or":[73],"relation.":[74],"The":[75],"inequalities":[78,130,146],"for":[79,131],"connectivity":[80,132],"have":[81],"been":[82],"studied":[83],"by":[84],"several":[85],"authors.":[86],"For":[87],"bipartite":[89,100,108,134,138],"with":[94,110],"bipartition":[95],"([Formula:":[96],"text]),":[98],"complementary":[101,139],"text].":[121],"this":[123],"paper,":[124],"we":[125,142],"obtain":[126],"graphs":[135],"graphs.":[140],"Furthermore,":[141],"prove":[143],"that":[144],"these":[145],"are":[147],"best":[148],"possible.":[149]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}