{"id":"https://openalex.org/W4283320317","doi":"https://doi.org/10.1051/ro/2022108","title":"Nordhaus\u2013Gaddum type inequalities on the total Italian domination number in graphs","display_name":"Nordhaus\u2013Gaddum type inequalities on the total Italian domination number in graphs","publication_year":2022,"publication_date":"2022-06-23","ids":{"openalex":"https://openalex.org/W4283320317","doi":"https://doi.org/10.1051/ro/2022108"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2022108","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022108","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/04/ro220127.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/04/ro220127.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023197041","display_name":"Seyed Mahmoud Sheikholeslami","orcid":"https://orcid.org/0000-0003-2298-4744"},"institutions":[{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Seyed Mahmoud Sheikholeslami","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran"],"raw_orcid":"https://orcid.org/0000-0003-2298-4744","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran","institution_ids":["https://openalex.org/I51301133"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036519893","display_name":"Lutz Volkmann","orcid":"https://orcid.org/0000-0003-3496-277X"},"institutions":[{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Lutz Volkmann","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran","institution_ids":["https://openalex.org/I51301133"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I51301133"],"apc_list":null,"apc_paid":null,"fwci":0.4311,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63420817,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"56","issue":"4","first_page":"2235","last_page":"2243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.963100016117096,"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":0.9581999778747559,"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":0.8377600312232971},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7558677792549133},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7263782024383545},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6996960639953613},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6708820462226868},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.6101946830749512},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5320290923118591},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3233112692832947}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8377600312232971},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7558677792549133},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7263782024383545},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6996960639953613},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6708820462226868},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.6101946830749512},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5320290923118591},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3233112692832947}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ro/2022108","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022108","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/04/ro220127.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:edpsciences.org:dkey/10.1051/ro/2022108","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1051/ro/2022108","raw_type":"Text"},{"id":"pmh:oai:numdam.org:RO_2022__56_4_2235_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2022108/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1051/ro/2022108","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022108","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/04/ro220127.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283320317.pdf","grobid_xml":"https://content.openalex.org/works/W4283320317.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1967557055","https://openalex.org/W1984228559","https://openalex.org/W2028333952","https://openalex.org/W2064817437","https://openalex.org/W2202070217","https://openalex.org/W2504650782","https://openalex.org/W2736718309","https://openalex.org/W2803382364","https://openalex.org/W2990268749","https://openalex.org/W3020124305","https://openalex.org/W3043697555","https://openalex.org/W3088905041","https://openalex.org/W3093787833","https://openalex.org/W3130237064","https://openalex.org/W3152577304","https://openalex.org/W3170816160","https://openalex.org/W4214937823","https://openalex.org/W4247328731"],"related_works":["https://openalex.org/W4362737182","https://openalex.org/W2104330975","https://openalex.org/W1621490777","https://openalex.org/W4285261572","https://openalex.org/W2611334166","https://openalex.org/W2962975014","https://openalex.org/W2010333092","https://openalex.org/W4307385446","https://openalex.org/W2012379512","https://openalex.org/W2904724461"],"abstract_inverted_index":{"Let":[0],"G":[1,10,21,29,113,118],"be":[2],"a":[3,19,23,51,95,116,124],"graph":[4,20,117],"with":[5,41,54,68,85,98],"vertex":[6,39,52,83,96],"set":[7],"V":[8,27],"(":[9,28,43,56,70,75,87,100,112],").":[11],"A":[12],"total":[13,106,125,139],"Italian":[14,107,126,140],"dominating":[15,127],"function":[16,24],"(TIDF)":[17],"on":[18,115],"is":[22,48,92,119],"f":[25,42,55,69,74,86,99],":":[26],")":[30,45,58,72,77,89,102,114],"\u2192":[31],"{0,":[32],"1,":[33,79],"2}":[34],"such":[35],"that":[36],"(i)":[37],"every":[38,82],"v":[40,44,84,88],"=":[46,59,73,78],"0":[47],"adjacent":[49,93],"to":[50,62,94],"u":[53,57,97,101],"2":[60],"or":[61],"two":[63],"vertices":[64],"w":[65,71],"and":[66,80],"z":[67,76],"(ii)":[81],"\u2265":[90,103],"1":[91],"1.":[104],"The":[105],"domination":[108,141],"number":[109],"\u03b3":[110],"tI":[111],"the":[120,138],"minimum":[121],"weight":[122],"of":[123],"function.":[128],"In":[129],"this":[130],"paper,":[131],"we":[132],"present":[133],"Nordhaus\u2013Gaddum":[134],"type":[135],"inequalities":[136],"for":[137],"number.":[142]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}
