{"id":"https://openalex.org/W3167774038","doi":"https://doi.org/10.1051/ro/2022089","title":"Restrained double Roman domination of a graph","display_name":"Restrained double Roman domination of a graph","publication_year":2022,"publication_date":"2022-05-31","ids":{"openalex":"https://openalex.org/W3167774038","doi":"https://doi.org/10.1051/ro/2022089","mag":"3167774038"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2022089","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022089","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/04/ro210262.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/ro210262.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059518359","display_name":"Doost Ali Mojdeh","orcid":"https://orcid.org/0000-0001-9373-3390"},"institutions":[{"id":"https://openalex.org/I4871159","display_name":"University of Mazandaran","ror":"https://ror.org/05fp9g671","country_code":"IR","type":"education","lineage":["https://openalex.org/I4871159"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Doost Ali Mojdeh","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran"],"raw_orcid":"https://orcid.org/0000-0001-9373-3390","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran","institution_ids":["https://openalex.org/I4871159"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032999279","display_name":"\u0130man Masoumi","orcid":"https://orcid.org/0000-0002-5215-615X"},"institutions":[{"id":"https://openalex.org/I9570713","display_name":"Tafresh University","ror":"https://ror.org/040f6ar92","country_code":"IR","type":"education","lineage":["https://openalex.org/I9570713"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Iman Masoumi","raw_affiliation_strings":["Department of Mathematics, University of Tafresh, Tafresh, Iran"],"raw_orcid":"https://orcid.org/0000-0002-5215-615X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Tafresh, Tafresh, Iran","institution_ids":["https://openalex.org/I9570713"]}]},{"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/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lutz Volkmann","raw_affiliation_strings":["Lehrstuhl II f\u00fcr Mathematik, RWTH Aachen University, 52056 Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl II f\u00fcr Mathematik, RWTH Aachen University, 52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4369,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.82833522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"56","issue":"4","first_page":"2293","last_page":"2304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9934999942779541,"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/T12288","display_name":"Optimization and Search Problems","score":0.9872000217437744,"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":0.8278906345367432},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7408921122550964},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6751279830932617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6439796090126038},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6239792108535767},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43405407667160034},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4161977767944336}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8278906345367432},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7408921122550964},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6751279830932617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6439796090126038},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6239792108535767},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43405407667160034},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4161977767944336},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ro/2022089","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022089","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/04/ro210262.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/2022089","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/2022089","raw_type":"Text"},{"id":"pmh:oai:numdam.org:RO_2022__56_4_2293_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2022089/","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/2022089","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022089","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/04/ro210262.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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3167774038.pdf","grobid_xml":"https://content.openalex.org/works/W3167774038.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1479863711","https://openalex.org/W1493071618","https://openalex.org/W1690464411","https://openalex.org/W1885115167","https://openalex.org/W2003370404","https://openalex.org/W2026300475","https://openalex.org/W2058946695","https://openalex.org/W2059358913","https://openalex.org/W2073661823","https://openalex.org/W2084981300","https://openalex.org/W2092586594","https://openalex.org/W2103411036","https://openalex.org/W2131269652","https://openalex.org/W2139312684","https://openalex.org/W2202070217","https://openalex.org/W2346913169","https://openalex.org/W2401610261","https://openalex.org/W2790637388","https://openalex.org/W2794674653","https://openalex.org/W2796421782","https://openalex.org/W2909548558","https://openalex.org/W3008183860","https://openalex.org/W3088905041","https://openalex.org/W3130237064"],"related_works":["https://openalex.org/W2383129606","https://openalex.org/W2953046811","https://openalex.org/W2104330975","https://openalex.org/W3135985610","https://openalex.org/W4362737182","https://openalex.org/W1987743836","https://openalex.org/W2910132672","https://openalex.org/W2024094529","https://openalex.org/W2023454821","https://openalex.org/W4292122332"],"abstract_inverted_index":{"For":[0],"a":[1,10,17,113,141,194],"graph":[2,196],"G":[3,96,148,157,197,204],"=":[4,36,61,69,127],"(":[5,33,58,66,84,124,133],"V":[6,21,98,125,131],",":[7],"E":[8],"),":[9,135],"restrained":[11,114,142,151,164,188,215,221,231],"double":[12,115,143,152,165,189,216,232],"Roman":[13,116,144,153,166,190,217,222,233],"dominating":[14,117,145],"function":[15,18,118,146],"is":[16,120,149,177],"f":[19,32,51,57,65,83,119,123,132],":":[20],"\u2192":[22],"{0,":[23],"1,":[24,70],"2,":[25,88],"3}":[26],"having":[27],"the":[28,39,72,91,94,121,137,150,161,171,187,201,207,214,220,227,230,242],"property":[29],"that":[30,170],"if":[31,64],"v":[34,41,67,74,129,134],")":[35,60,68,86,126],"0,":[37],"then":[38,71],"vertex":[40,73],"must":[42,75],"have":[43,76],"at":[44,77,90],"least":[45,78],"two":[46],"neighbors":[47],"assigned":[48],"2":[49],"under":[50],"or":[52],"one":[53,79],"neighbor":[54,80],"w":[55,59,81,85],"with":[56,82,103,168],"3,":[62],"and":[63,89,136,205,237],"\u2265":[87],"same":[92],"time,":[93],"subgraph":[95],"[":[97],"0]":[99],"which":[100],"includes":[101],"vertices":[102],"zero":[104],"labels":[105],"has":[106],"no":[107],"isolated":[108],"vertex.":[109],"The":[110],"weight":[111,139],"of":[112,140,156,163,173,193,200,203,235],"sum":[122],"\u2211":[128],"\u2208":[130],"minimum":[138],"on":[147,186],"domination":[154,167,191,218,234],"number":[155,192],".":[158],"We":[159,212],"initiate":[160],"study":[162,213],"proving":[169],"problem":[172],"computing":[174],"this":[175,210],"parameter":[176],"NP":[178],"-hard.":[179],"Then":[180],"we":[181,225],"present":[182],"an":[183],"upper":[184],"bound":[185],"connected":[195],"in":[198],"terms":[199],"order":[202],"characterize":[206],"graphs":[208],"attaining":[209,241],"bound.":[211],"versus":[219],"domination.":[223],"Finally,":[224],"investigate":[226],"bounds":[228],"for":[229],"trees":[236,239],"determine":[238],"T":[240],"exhibited":[243],"bounds.":[244]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}