{"id":"https://openalex.org/W1973144078","doi":"https://doi.org/10.1142/s1793830914500451","title":"Relations between the Roman k-domination and Roman domination numbers in graphs","display_name":"Relations between the Roman k-domination and Roman domination numbers in graphs","publication_year":2014,"publication_date":"2014-04-21","ids":{"openalex":"https://openalex.org/W1973144078","doi":"https://doi.org/10.1142/s1793830914500451","mag":"1973144078"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830914500451","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500451","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5000732408","display_name":"Ahmed Bouchou","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128965","display_name":"University Yahia Fares of Medea","ror":"https://ror.org/02e2yc259","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210128965"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Ahmed Bouchou","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of M\u00e9d\u00e9a, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of M\u00e9d\u00e9a, Algeria","institution_ids":["https://openalex.org/I4210128965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085691353","display_name":"Mostafa Blidia","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":"Mostafa Blidia","raw_affiliation_strings":["LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria"],"raw_orcid":null,"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":"last","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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria","institution_ids":["https://openalex.org/I83332908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7343,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7077142,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"06","issue":"03","first_page":"1450045","last_page":"1450045"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9979000091552734,"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":0.9979000091552734,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9696000218391418,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9653000235557556,"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":0.8629608154296875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7275518178939819},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6764259934425354},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6065862774848938},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5498794913291931},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.46345704793930054},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.4482038617134094},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.042879730463027954}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8629608154296875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7275518178939819},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6764259934425354},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6065862774848938},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5498794913291931},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.46345704793930054},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.4482038617134094},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.042879730463027954},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830914500451","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500451","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W174831056","https://openalex.org/W1566493102","https://openalex.org/W1963724532","https://openalex.org/W1976161279","https://openalex.org/W1984228559","https://openalex.org/W2019578481","https://openalex.org/W2048025378","https://openalex.org/W2058946695","https://openalex.org/W2137906639","https://openalex.org/W2140273161","https://openalex.org/W2739951829","https://openalex.org/W4247549312","https://openalex.org/W4251005761"],"related_works":["https://openalex.org/W2794522194","https://openalex.org/W2963404550","https://openalex.org/W30750922","https://openalex.org/W4378234127","https://openalex.org/W72870998","https://openalex.org/W2763279932","https://openalex.org/W2339280209","https://openalex.org/W2346500824","https://openalex.org/W4299822763","https://openalex.org/W2790637388"],"abstract_inverted_index":{"Let":[0],"G":[1,23,96,163],"=":[2,42,64,68,83,168],"(V,":[3],"E)":[4],"be":[5,11],"a":[6,12,25,139],"graph":[7],"and":[8,87,118,145,157],"let":[9],"k":[10,49,59],"positive":[13],"integer.":[14],"A":[15],"Roman":[16,100],"k-dominating":[17],"function":[18,26],"(":[19],"R":[20,77,93,120,147,170],"k-DF)":[21],"on":[22,95],"is":[24,44,79,97],"f":[27],":":[28],"V(G)":[29],"\u2192":[30],"{0,":[31],"1,":[32,69],"2}":[33],"such":[34,161],"that":[35],"every":[36],"vertex":[37],"u":[38],"for":[39,66,149],"which":[40],"f(u)":[41,86],"0":[43],"adjacent":[45],"to":[46],"at":[47],"least":[48],"vertices":[50],"v":[51,54,58],"1":[52],",":[53,56,152],"2":[55,65],"\u2026,":[57,71],"with":[60,164],"f(v":[61],"i":[62,67],")":[63],"2,":[70],"k.":[72],"The":[73],"weight":[74,90],"of":[75,91,106,126,129],"an":[76,92],"k-DF":[78,94],"the":[80,88,99],"value":[81],"f(V(G))":[82],"\u2211":[84],"u\u2208V(G)":[85],"minimum":[89],"called":[98],"k-domination":[101],"number":[102],"\u03b3":[103,115,119,142,146,165,169],"kR":[104,116,143,166],"(G)":[105,117,144,148,167],"G.":[107],"In":[108],"this":[109],"paper,":[110],"we":[111,123,137,158],"present":[112],"relations":[113],"between":[114,141],"(G).":[121],"Moreover,":[122],"give":[124],"characterizations":[125],"some":[127],"classes":[128],"graphs":[130,156,162],"attaining":[131],"equality":[132],"in":[133],"these":[134],"relations.":[135],"Finally,":[136],"establish":[138],"relation":[140],"{K":[150],"1,3":[151,154],"K":[153],"+e}-free":[155],"characterize":[159],"all":[160],"(G)+t,":[171],"where":[172],"[Formula:":[173],"see":[174],"text].":[175]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}