{"id":"https://openalex.org/W4320483964","doi":"https://doi.org/10.1051/ro/2023017","title":"Independent Roman bondage of graphs","display_name":"Independent Roman bondage of graphs","publication_year":2023,"publication_date":"2023-02-13","ids":{"openalex":"https://openalex.org/W4320483964","doi":"https://doi.org/10.1051/ro/2023017"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2023017","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023017","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2023/02/ro220476.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"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":"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/2023/02/ro220476.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062707037","display_name":"Saeed Kosari","orcid":"https://orcid.org/0000-0002-1427-5473"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Saeed Kosari","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061538318","display_name":"Jafar Amjadi","orcid":"https://orcid.org/0000-0001-9340-4773"},"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":"Jafar Amjadi","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"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008747635","display_name":"Mustapha Chellali","orcid":null},"institutions":[{"id":"https://openalex.org/I83332908","display_name":"University of Blida","ror":"https://ror.org/03g41pw14","country_code":"DZ","type":"education","lineage":["https://openalex.org/I83332908"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mustapha Chellali","raw_affiliation_strings":["LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria","institution_ids":["https://openalex.org/I83332908"]}]},{"author_position":"last","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"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5062707037"],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":null,"apc_paid":null,"fwci":0.388,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61325013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"57","issue":"2","first_page":"371","last_page":"382"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9901999831199646,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9056103825569153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7742291688919067},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7251877784729004},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6472043991088867},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5565822124481201},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5143603086471558},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.4857516884803772},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4513588547706604},{"id":"https://openalex.org/keywords/weight-function","display_name":"Weight function","score":0.44827720522880554},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44380804896354675},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41129791736602783},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3563602566719055},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05262371897697449}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9056103825569153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742291688919067},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7251877784729004},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6472043991088867},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5565822124481201},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5143603086471558},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.4857516884803772},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4513588547706604},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.44827720522880554},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44380804896354675},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41129791736602783},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3563602566719055},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05262371897697449},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2023017","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023017","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2023/02/ro220476.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"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":"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/2023017","is_oa":true,"landing_page_url":null,"pdf_url":"https://www.rairo-ro.org/10.1051/ro/2023017/pdf","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/2023017","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1051/ro/2023017","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023017","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2023/02/ro220476.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"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":"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/16","display_name":"Peace, Justice and strong institutions","score":0.5699999928474426}],"awards":[{"id":"https://openalex.org/G5640046168","display_name":null,"funder_award_id":"622274","funder_id":"https://openalex.org/F4320325431","funder_display_name":"Wuhan University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320324116","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17"},{"id":"https://openalex.org/F4320325431","display_name":"Wuhan University of Science and Technology","ror":"https://ror.org/00e4hrk88"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4320483964.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1593700485","https://openalex.org/W1984228559","https://openalex.org/W1987826317","https://openalex.org/W1993155410","https://openalex.org/W2007168254","https://openalex.org/W2036334548","https://openalex.org/W2060569445","https://openalex.org/W2078588121","https://openalex.org/W2128791726","https://openalex.org/W2770588060","https://openalex.org/W3011796432","https://openalex.org/W3043697555","https://openalex.org/W3093787833","https://openalex.org/W3096221061","https://openalex.org/W3104882513","https://openalex.org/W4205699039","https://openalex.org/W4214937823"],"related_works":["https://openalex.org/W2471372608","https://openalex.org/W2049514974","https://openalex.org/W103840660","https://openalex.org/W4301055422","https://openalex.org/W2408555533","https://openalex.org/W2504650782","https://openalex.org/W2740775687","https://openalex.org/W3128085997","https://openalex.org/W2589726528","https://openalex.org/W3005171979"],"abstract_inverted_index":{"An":[0],"independent":[1,86,116,180],"Roman":[2,87,117,181],"dominating":[3],"function":[4,12,79],"(IRD-function)":[5],"on":[6,104,193,206,251],"a":[7,11,126],"graph":[8,127],"G":[9,17,93,96,105,123,128,152,159,167,197],"is":[10,39,67,74,97,184,223],"f":[13,33,49,66],":":[14],"V":[15],"(":[16,34,50,92,122,151,158,166,196,228],")":[18,36,52,94,124,153,162,198,230],"\u2192":[19],"{0,":[20],"1,":[21],"2}":[22],"satisfying":[23],"the":[24,57,75,85,98,112,115,141,174,179,238,245,252,255],"conditions":[25],"that":[26,173,225],"(i)":[27],"every":[28],"vertex":[29,45],"u":[30,35],"for":[31,47,154,186,208,214,234],"which":[32,48,155],"=":[37,53],"0":[38],"adjacent":[40],"to":[41],"at":[42,130,136,219],"least":[43,131,137,220],"one":[44,132],"v":[46,51],"2,":[54],"and":[55,84],"(ii)":[56],"set":[58,145],"of":[59,71,77,95,101,114,125,134,144,146,217,244,254],"all":[60,82],"vertices":[61],"assigned":[62],"non-zero":[63],"values":[64,80,205],"under":[65],"independent.":[68],"The":[69],"weight":[70,100],"an":[72,102],"IRD-function":[73,103],"sum":[76],"its":[78],"over":[81],"vertices,":[83],"domination":[88],"number":[89,119],"i":[90,156,164],"R":[91,157,165],"minimum":[99],".":[106],"In":[107,212],"this":[108],"paper,":[109],"we":[110],"initiate":[111],"study":[113],"bondage":[118,182],"b":[120,194,226],"iR":[121,195,227],"having":[129],"component":[133],"order":[135,218],"three,":[138,221],"defined":[139],"as":[140,201,203],"smallest":[142],"size":[143],"edges":[147],"F":[148,161],"\u2286":[149],"E":[150],"\u2212":[160],"&gt;":[163],").":[168],"We":[169],"begin":[170],"by":[171],"showing":[172],"decision":[175],"problem":[176,183],"associated":[177],"with":[178,248],"NP-hard":[185],"bipartite":[187],"graphs.":[188,211],"Then":[189],"various":[190],"upper":[191,239],"bounds":[192,240],"are":[199,241],"established":[200],"well":[202],"exact":[204],"it":[207,222],"some":[209],"special":[210],"particular,":[213],"trees":[215],"T":[216,229],"shown":[224],"\u2264":[231],"3,":[232],"while":[233],"connected":[235],"planar":[236],"graphs":[237],"in":[242],"terms":[243],"maximum":[246],"degree":[247],"refinements":[249],"depending":[250],"girth":[253],"graph.":[256]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-02-03T23:48:18.283914","created_date":"2025-10-10T00:00:00"}
