{"id":"https://openalex.org/W2337802335","doi":"https://doi.org/10.1080/00207160.2015.1052804","title":"On maximal Roman domination in graphs","display_name":"On maximal Roman domination in graphs","publication_year":2015,"publication_date":"2015-05-20","ids":{"openalex":"https://openalex.org/W2337802335","doi":"https://doi.org/10.1080/00207160.2015.1052804","mag":"2337802335"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1052804","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1052804","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"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/I70876197","display_name":"Babol University of Medical Sciences","ror":"https://ror.org/02r5cmz65","country_code":"IR","type":"education","lineage":["https://openalex.org/I70876197"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Hossein Abdollahzadeh Ahangar","raw_affiliation_strings":[",","Department of Basic Science, Babol University of Technology, Babol, Iran"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Department of Basic Science, Babol University of Technology, Babol, Iran","institution_ids":["https://openalex.org/I70876197"]}]},{"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":",","institution_ids":[]},{"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/A5065127626","display_name":"Dorota Kuziak","orcid":"https://orcid.org/0000-0001-9660-3284"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Dorota Kuziak","raw_affiliation_strings":[",","Departament d'Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Tarragona, Spain"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Departament d'Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]}]},{"author_position":"last","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., 1046 Sofia, Bulgaria"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Hristo Smirnenski 1 Blv., 1046 Sofia, Bulgaria","institution_ids":["https://openalex.org/I206451062"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066590366"],"corresponding_institution_ids":["https://openalex.org/I70876197"],"apc_list":null,"apc_paid":null,"fwci":0.3505,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.67793594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"93","issue":"7","first_page":"1093","last_page":"1102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9962000250816345,"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":0.9915000200271606,"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":0.8609646558761597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8151130676269531},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7257121801376343},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6733716726303101},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6352741718292236},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5379418134689331},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5102169513702393},{"id":"https://openalex.org/keywords/rdf","display_name":"RDF","score":0.4544350504875183},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.4386313855648041},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39246031641960144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05881863832473755}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8609646558761597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8151130676269531},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7257121801376343},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6733716726303101},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6352741718292236},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5379418134689331},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5102169513702393},{"id":"https://openalex.org/C147497476","wikidata":"https://www.wikidata.org/wiki/Q54872","display_name":"RDF","level":3,"score":0.4544350504875183},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.4386313855648041},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39246031641960144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05881863832473755},{"id":"https://openalex.org/C2129575","wikidata":"https://www.wikidata.org/wiki/Q54837","display_name":"Semantic Web","level":2,"score":0.0},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1052804","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1052804","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1493071618","https://openalex.org/W1581552469","https://openalex.org/W1984228559","https://openalex.org/W1994990018","https://openalex.org/W2019578481","https://openalex.org/W2058946695","https://openalex.org/W2059179208","https://openalex.org/W2592437091","https://openalex.org/W2616042493","https://openalex.org/W2624473290","https://openalex.org/W4251005761"],"related_works":["https://openalex.org/W2794522194","https://openalex.org/W2963404550","https://openalex.org/W2984335350","https://openalex.org/W1123717642","https://openalex.org/W4312062610","https://openalex.org/W3217516113","https://openalex.org/W4226354266","https://openalex.org/W2736530170","https://openalex.org/W4313020364","https://openalex.org/W2034961945"],"abstract_inverted_index":{"A":[0,65],"Roman":[1,59,89],"dominating":[2,83],"function":[3,11],"(RDF)":[4],"for":[5,22,35,55,68,105,115],"a":[6,10,41,53,69,73,82,94,102,142],"graph":[7,70,95,118],"G=(V,E)":[8],"is":[9,25,44,57,72,80,120],"f:V\u2192{0,1,2}":[12],"satisfying":[13],"the":[14,45,49,58,98,112],"condition":[15],"that":[16,77,110,137,152],"every":[17],"vertex":[18,31],"u":[19],"of":[20,33,40,52,63,85,93,101,144,148],"G":[21,34,56,71,96,119,135],"which":[23,36],"f(u)=0":[24],"adjacent":[26],"to":[27,125],"at":[28],"least":[29],"one":[30],"v":[32],"f(v)=2.":[37],"The":[38,87],"weight":[39,51,100],"RDF":[42,54,67,74,104],"f":[43,75],"sum":[46],"f(V)=\u2211v\u2208Vf(v),":[47],"and":[48],"minimum":[50,99],"domination":[60,90],"number,":[61,91],"\u03b3R(G),":[62],"G.":[64,86,106],"maximal":[66,88,103],"such":[76,136,151],"V0={w\u2208V|":[78],"f(w)=0}":[79],"not":[81],"set":[84],"\u03b3mR(G),":[92],"equals":[97],"We":[107,139],"first":[108],"show":[109],"determining":[111],"number":[113],"\u03b3mR(G)":[114],"an":[116],"arbitrary":[117],"NP-complete":[121],"even":[122],"when":[123],"restricted":[124],"bipartite":[126],"or":[127],"planar":[128],"graphs.":[129],"Then,":[130],"we":[131],"characterize":[132],"connected":[133],"graphs":[134],"\u03b3mR(G)=\u03b3R(G).":[138],"also":[140],"provide":[141],"characterization":[143],"all":[145],"trees":[146],"T":[147],"order":[149],"n":[150],"\u03b3mR(T)=n\u22122.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
