{"id":"https://openalex.org/W4389922002","doi":"https://doi.org/10.3390/axioms12121134","title":"Equitable and Paired Equitable Domination in Inflated Graphs and Their Complements","display_name":"Equitable and Paired Equitable Domination in Inflated Graphs and Their Complements","publication_year":2023,"publication_date":"2023-12-18","ids":{"openalex":"https://openalex.org/W4389922002","doi":"https://doi.org/10.3390/axioms12121134"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12121134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121134","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1134/pdf?version=1703226215","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/12/1134/pdf?version=1703226215","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101584855","display_name":"N. Kumaran","orcid":null},"institutions":[{"id":"https://openalex.org/I1330855593","display_name":"Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology","ror":"https://ror.org/05bc5bx80","country_code":"IN","type":"education","lineage":["https://openalex.org/I1330855593"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Narayanan Kumaran","raw_affiliation_strings":["Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India","institution_ids":["https://openalex.org/I1330855593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113215421","display_name":"Meenakshi Annamalai","orcid":null},"institutions":[{"id":"https://openalex.org/I1330855593","display_name":"Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology","ror":"https://ror.org/05bc5bx80","country_code":"IN","type":"education","lineage":["https://openalex.org/I1330855593"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Annamalai Meenakshi","raw_affiliation_strings":["Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India","institution_ids":["https://openalex.org/I1330855593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086551021","display_name":"R\u00f3bert \u010cep","orcid":"https://orcid.org/0000-0001-9610-4215"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Robert Cep","raw_affiliation_strings":["Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0001-9610-4215","affiliations":[{"raw_affiliation_string":"Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082065860","display_name":"J. Udaya Prakash","orcid":null},"institutions":[{"id":"https://openalex.org/I1330855593","display_name":"Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology","ror":"https://ror.org/05bc5bx80","country_code":"IN","type":"education","lineage":["https://openalex.org/I1330855593"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jayavelu Udaya Prakash","raw_affiliation_strings":["Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India"],"raw_orcid":"https://orcid.org/0000-0001-9229-5499","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India","institution_ids":["https://openalex.org/I1330855593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010551503","display_name":"Ond\u0159ej Mizera","orcid":"https://orcid.org/0000-0002-3528-8951"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Ondrej Mizera","raw_affiliation_strings":["Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-3528-8951","affiliations":[{"raw_affiliation_string":"Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5086551021"],"corresponding_institution_ids":["https://openalex.org/I142208455"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25045832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"12","first_page":"1134","last_page":"1134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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":0.9994000196456909,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9757000207901001,"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":0.9602000117301941,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6378235816955566},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6342462301254272},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6321839094161987},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5785648822784424},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5413640737533569},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40326160192489624}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6378235816955566},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6342462301254272},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6321839094161987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5785648822784424},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5413640737533569},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40326160192489624}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12121134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121134","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1134/pdf?version=1703226215","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:dspace.vsb.cz:10084/152702","is_oa":true,"landing_page_url":"http://hdl.handle.net/10084/152702","pdf_url":"http://dspace.vsb.cz/bitstream/10084/152702/1/2075-1680-2023v12i12an1134.pdf","source":{"id":"https://openalex.org/S4306401668","display_name":"DSpace V\u0160B-TUO (V\u0160B-TUO)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142208455","host_organization_name":"VSB - Technical University of Ostrava","host_organization_lineage":["https://openalex.org/I142208455"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:doaj.org/article:33e3635e774f4c66afb3d02e0e9d7cfa","is_oa":true,"landing_page_url":"https://doaj.org/article/33e3635e774f4c66afb3d02e0e9d7cfa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 12, p 1134 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12121134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121134","pdf_url":"https://www.mdpi.com/2075-1680/12/12/1134/pdf?version=1703226215","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G2586507490","display_name":null,"funder_award_id":"SP2023/088","funder_id":"https://openalex.org/F4320321005","funder_display_name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy"}],"funders":[{"id":"https://openalex.org/F4320321005","display_name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy","ror":"https://ror.org/037n8p820"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389922002.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W174616216","https://openalex.org/W1484040084","https://openalex.org/W2027818420","https://openalex.org/W2045481823","https://openalex.org/W2066561381","https://openalex.org/W2068079716","https://openalex.org/W2187675617","https://openalex.org/W2587625905","https://openalex.org/W2955252909","https://openalex.org/W3110267038","https://openalex.org/W3212838666","https://openalex.org/W4232031581","https://openalex.org/W4247549312","https://openalex.org/W4288826047","https://openalex.org/W6607081781","https://openalex.org/W6687301683"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2963404550","https://openalex.org/W2794522194","https://openalex.org/W1976691234","https://openalex.org/W2963176699","https://openalex.org/W2888180870","https://openalex.org/W30750922","https://openalex.org/W4205905997","https://openalex.org/W4378234127","https://openalex.org/W3111310291"],"abstract_inverted_index":{"Domination":[0],"plays":[1],"an":[2,44],"indispensable":[3],"role":[4],"in":[5,131],"graph":[6,46,73,89],"theory.":[7],"Various":[8],"types":[9,14],"of":[10,15,34,43,55,68,70,108,111,121,124],"domination":[11,33,53,60,66,116],"explore":[12],"various":[13,132],"applications.":[16],"Equal-status":[17],"people":[18],"work":[19],"together":[20],"and":[21,40,62,97,106,114,134],"interlace":[22],"with":[23,90],"each":[24],"other":[25],"easily.":[26],"In":[27],"this":[28,109],"paper,":[29],"the":[30,52,56,58,63,71,79,119,122,125,137],"paired":[31,64,112],"equitable":[32,59,65,113,115],"a":[35,88],"graph,":[36,39,57],"its":[37,41],"inflated":[38,45,72],"complement":[42],"were":[47,74],"studied.":[48],"The":[49,104],"relationship":[50],"between":[51],"number":[54,67],"number,":[61],"complements":[69],"established.":[75],"Furthermore,":[76],"we":[77],"proved":[78],"Nordhaus\u2013Gaddum-type":[80],"inequality,":[81],"that":[82],"is,":[83],"\u03b3pre(H)+\u03b3pre(H)\u22646":[84],"if":[85],"H":[86],"is":[87],"m":[91],"nodes":[92],"where":[93],"m\u22610,":[94],"2(mod":[95],"8)":[96],"d(ai)":[98],"=":[99],"(m/2)":[100],"for":[101],"all":[102],"ai.":[103],"challenges":[105],"limitations":[107],"parameter":[110],"depends":[117],"on":[118],"degree":[120],"vertex":[123],"graph.":[126],"Practical":[127],"applications":[128],"are":[129],"discussed":[130],"fields":[133],"illustrated":[135],"using":[136],"studied":[138],"parameter.":[139]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
