{"id":"https://openalex.org/W3016594015","doi":"https://doi.org/10.1051/ro/2020038","title":"Some progress on the mixed roman domination in graphs","display_name":"Some progress on the mixed roman domination in graphs","publication_year":2020,"publication_date":"2020-04-17","ids":{"openalex":"https://openalex.org/W3016594015","doi":"https://doi.org/10.1051/ro/2020038","mag":"3016594015"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2020038","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2020038","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2021/01/ro180193.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"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":null,"license_id":null,"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":"bronze","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2021/01/ro180193.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066590366","display_name":"H. Abdollahzadeh Ahangar","orcid":"https://orcid.org/0000-0002-0038-8047"},"institutions":[{"id":"https://openalex.org/I84248293","display_name":"Babol Noshirvani University of Technology","ror":"https://ror.org/02zc85170","country_code":"IR","type":"education","lineage":["https://openalex.org/I84248293"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Hossein Abdollahzadeh Ahangar","raw_affiliation_strings":["Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol 47148-71167, I.R. Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol 47148-71167, I.R. Iran","institution_ids":["https://openalex.org/I84248293"]}]},{"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"],"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":"https://orcid.org/0000-0001-5231-6195"},"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, B.P. 270, Blida, Algeria"],"affiliations":[{"raw_affiliation_string":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria","institution_ids":["https://openalex.org/I83332908"]}]},{"author_position":"middle","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":false,"raw_author_name":"Saeed Kosari","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China"],"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/A5027008906","display_name":"Vladimir Samodivkin","orcid":"https://orcid.org/0000-0001-7934-5789"},"institutions":[{"id":"https://openalex.org/I206451062","display_name":"University of Architecture, Civil Engineering and Geodesy","ror":"https://ror.org/033cz7157","country_code":"BG","type":"education","lineage":["https://openalex.org/I206451062"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Vladimir Samodivkin","raw_affiliation_strings":["Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Hristo Smirnenski 1 Blv., Sofia 1046, Bulgaria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Hristo Smirnenski 1 Blv., Sofia 1046, Bulgaria","institution_ids":["https://openalex.org/I206451062"]}]},{"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"],"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":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5066590366"],"corresponding_institution_ids":["https://openalex.org/I84248293"],"apc_list":null,"apc_paid":null,"fwci":0.289,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61356383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"55","issue":null,"first_page":"S1411","last_page":"S1423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9984999895095825,"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":0.9901999831199646,"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":0.8610917925834656},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7599968910217285},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6673907041549683},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.664535641670227},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6404922604560852},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5819189548492432},{"id":"https://openalex.org/keywords/weight-function","display_name":"Weight function","score":0.5648477673530579},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5023832321166992},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.4622696340084076},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4215739369392395},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.4185003340244293}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8610917925834656},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7599968910217285},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6673907041549683},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.664535641670227},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6404922604560852},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5819189548492432},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.5648477673530579},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5023832321166992},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.4622696340084076},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4215739369392395},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.4185003340244293},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ro/2020038","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2020038","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2021/01/ro180193.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"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":null,"license_id":null,"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/2020038","is_oa":true,"landing_page_url":null,"pdf_url":"https://www.rairo-ro.org/10.1051/ro/2020038/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/2020038","raw_type":"Text"},{"id":"pmh:oai:numdam.org:RO_2021__55_S1_S1411_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2020038/","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/2020038","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2020038","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2021/01/ro180193.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1998669351","display_name":null,"funder_award_id":"BNUT/385001/99","funder_id":"https://openalex.org/F4320323590","funder_display_name":"Babol Noshirvani University of Technology"},{"id":"https://openalex.org/G7666721334","display_name":null,"funder_award_id":"BNUT/","funder_id":"https://openalex.org/F4320323590","funder_display_name":"Babol Noshirvani University of Technology"}],"funders":[{"id":"https://openalex.org/F4320323590","display_name":"Babol Noshirvani University of Technology","ror":"https://ror.org/02zc85170"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3016594015.pdf","grobid_xml":"https://content.openalex.org/works/W3016594015.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W166457437","https://openalex.org/W788806422","https://openalex.org/W1493071618","https://openalex.org/W1984228559","https://openalex.org/W2026300475","https://openalex.org/W2031491044","https://openalex.org/W2058946695","https://openalex.org/W2059179208","https://openalex.org/W2061470089","https://openalex.org/W2062915396","https://openalex.org/W2070924562","https://openalex.org/W2090663581","https://openalex.org/W2117222483","https://openalex.org/W2740775687","https://openalex.org/W2899096937","https://openalex.org/W2962825745","https://openalex.org/W2963745986","https://openalex.org/W2967176398","https://openalex.org/W2989759640","https://openalex.org/W3005478270","https://openalex.org/W3020124305","https://openalex.org/W3155635271","https://openalex.org/W4251005761"],"related_works":["https://openalex.org/W4226354266","https://openalex.org/W4312062610","https://openalex.org/W3217516113","https://openalex.org/W2963955554","https://openalex.org/W2790041388","https://openalex.org/W2061040604","https://openalex.org/W3045726094","https://openalex.org/W2611334166","https://openalex.org/W3210644741","https://openalex.org/W4224863994"],"abstract_inverted_index":{"Let":[0],"G":[1,26,104,107,119,133],"=":[2,53,72,87],"(":[3,103,132],"V,":[4],"E":[5,18,34,49,68,93],")":[6,86,105,134],"be":[7],"a":[8,28,77,113],"simple":[9],"graph":[10],"with":[11],"vertex":[12],"setxs":[13],"V":[14,32,47,66,91],"and":[15,140,145],"edge":[16],"set":[17],".":[19,95,120],"A":[20],"mixed":[21,78,97,114,150],"Roman":[22,79,98,115,151],"dominating":[23,80,116],"function":[24,29,81,117],"of":[25,76,106,112,118,127,155,161],"is":[27,55,83,108,135],"f":[30,82,85],":":[31],"\u222a":[33,48,67,92],"\u2192":[35],"{0,":[36],"1,":[37],"2}":[38],"satisfying":[39],"the":[40,109,125,149,159],"condition":[41],"that":[42,124],"every":[43],"element":[44,63],"x":[45,89],"\u2208":[46,65,90],"for":[50,69,137,158],"which":[51,70],"f(x)":[52,94],"0":[54],"adjacent":[56],"or":[57],"incident":[58],"to":[59],"at":[60],"least":[61],"one":[62],"y":[64],"f(y)":[71],"2.":[73],"The":[74,96],"weight":[75,111],"\u03c9(":[84],"\u2211":[88],"domination":[99,152],"number":[100],"\u03b3":[101,129],"R":[102,130],"minimum":[110],"We":[121],"first":[122],"show":[123],"problem":[126],"computing":[128],"*":[131],"NP-complete":[136],"bipartite":[138],"graphs":[139],"then":[141],"we":[142],"present":[143],"upper":[144],"lower":[146],"bounds":[147],"on":[148],"number,":[153],"some":[154],"them":[156],"are":[157],"class":[160],"trees.":[162]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
