{"id":"https://openalex.org/W4297060651","doi":"https://doi.org/10.1142/s1793830922501658","title":"On disjoint maximum and maximal independent sets in graphs and inverse independence number","display_name":"On disjoint maximum and maximal independent sets in graphs and inverse independence number","publication_year":2022,"publication_date":"2022-09-25","ids":{"openalex":"https://openalex.org/W4297060651","doi":"https://doi.org/10.1142/s1793830922501658"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922501658","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501658","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","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/A5083580469","display_name":"Fatma Kaci","orcid":"https://orcid.org/0000-0001-5019-7663"},"institutions":[{"id":"https://openalex.org/I206961696","display_name":"University of Biskra","ror":"https://ror.org/05fr5y859","country_code":"DZ","type":"education","lineage":["https://openalex.org/I206961696"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Fatma Kaci","raw_affiliation_strings":["Department of Mathematics, University of Mohamed Khider, B.P 145, Biskra, Algeria"],"raw_orcid":"https://orcid.org/0000-0001-5019-7663","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Mohamed Khider, B.P 145, Biskra, Algeria","institution_ids":["https://openalex.org/I206961696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083580469"],"corresponding_institution_ids":["https://openalex.org/I206961696"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14503872,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"08","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T11476","display_name":"Graph theory and applications","score":0.9961000084877014,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.995199978351593,"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/independence-number","display_name":"Independence number","score":0.7724370956420898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7593756318092346},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.733099102973938},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7330976128578186},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7318968176841736},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.6916468143463135},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.6748105883598328},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.6295079588890076},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.5581706166267395},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4929015636444092},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4445226192474365},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.21995753049850464},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16242781281471252},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.0738551914691925}],"concepts":[{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.7724370956420898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7593756318092346},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.733099102973938},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7330976128578186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7318968176841736},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.6916468143463135},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.6748105883598328},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6295079588890076},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.5581706166267395},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4929015636444092},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4445226192474365},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.21995753049850464},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16242781281471252},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.0738551914691925},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922501658","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501658","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2066049837","https://openalex.org/W2124512217","https://openalex.org/W2592437091"],"related_works":["https://openalex.org/W2152478214","https://openalex.org/W4383046435","https://openalex.org/W4297060651","https://openalex.org/W4313400216","https://openalex.org/W2188337468","https://openalex.org/W2741283207","https://openalex.org/W2068819940","https://openalex.org/W1969466213","https://openalex.org/W2741772349","https://openalex.org/W2029614947"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,109],"give":[4],"a":[5,36,50,107],"class":[6],"of":[7,22,35,86,106,124,134],"graphs":[8],"that":[9],"do":[10],"not":[11],"admit":[12],"disjoint":[13],"maximum":[14],"and":[15,29,97,118,131],"maximal":[16],"independent":[17,59,68,90],"(MMI)":[18],"sets.":[19],"The":[20,76],"concept":[21],"inverse":[23,67,77,89],"independence":[24,33,78,104],"was":[25],"introduced":[26],"by":[27,113],"Bhat":[28,30,96,98],"in":[31,54,92],"[Inverse":[32],"number":[34,79,105],"graph,":[37,108],"Int.":[38],"J.":[39],"Comput.":[40],"Appl.":[41],"42(5)":[42],"(2012)":[43],"9\u201313].":[44],"Let":[45],"[Formula:":[46,51,55,61,73,80,93],"see":[47,52,56,62,74,81,94],"text]":[48,63,82],"be":[49],"text]-set":[53],"text].":[57,75,95],"An":[58],"set":[60,69,91],"is":[64,83],"called":[65],"an":[66],"with":[70],"respect":[71],"to":[72],"the":[84,87,103,111,128],"size":[85],"largest":[88],"gave":[99],"few":[100],"bounds":[101,117],"on":[102],"continue":[110],"study":[112],"giving":[114],"some":[115],"new":[116],"exact":[119],"value":[120],"for":[121],"particular":[122,136],"classes":[123],"graphs:":[125],"spider":[126],"tree,":[127],"rooted":[129],"product":[130,133],"Cartesian":[132],"two":[135],"graphs.":[137]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}