{"id":"https://openalex.org/W4313404104","doi":"https://doi.org/10.1080/09728600.2022.2158051","title":"Quasi-total Roman reinforcement in graphs","display_name":"Quasi-total Roman reinforcement in graphs","publication_year":2022,"publication_date":"2022-12-19","ids":{"openalex":"https://openalex.org/W4313404104","doi":"https://doi.org/10.1080/09728600.2022.2158051"},"language":"en","primary_location":{"id":"doi:10.1080/09728600.2022.2158051","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2158051","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1080/09728600.2022.2158051","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048610567","display_name":"N. Ebrahimi","orcid":null},"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":true,"raw_author_name":"N. Ebrahimi","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran","institution_ids":["https://openalex.org/I51301133"]}]},{"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":"J. Amjadi","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, 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":"M. Chellali","raw_affiliation_strings":["LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria"],"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":"S.M. Sheikholeslami","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran","institution_ids":["https://openalex.org/I51301133"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048610567"],"corresponding_institution_ids":["https://openalex.org/I51301133"],"apc_list":{"value":1000,"currency":"GBP","value_usd":1226},"apc_paid":{"value":1000,"currency":"GBP","value_usd":1226},"fwci":0.4382,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66566061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"20","issue":"1","first_page":"1","last_page":"8"},"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":0.9994000196456909,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9882000088691711,"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":0.8035444021224976},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7630909085273743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7313327789306641},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.652852475643158},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5491575598716736},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.503452479839325},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47622400522232056},{"id":"https://openalex.org/keywords/reinforcement","display_name":"Reinforcement","score":0.46641600131988525},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41607218980789185}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8035444021224976},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7630909085273743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7313327789306641},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.652852475643158},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5491575598716736},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.503452479839325},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47622400522232056},{"id":"https://openalex.org/C67203356","wikidata":"https://www.wikidata.org/wiki/Q1321905","display_name":"Reinforcement","level":2,"score":0.46641600131988525},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41607218980789185},{"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/09728600.2022.2158051","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2158051","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:400dc800a3574cdbb56d64a6ca4ba8d8","is_oa":true,"landing_page_url":"https://doaj.org/article/400dc800a3574cdbb56d64a6ca4ba8d8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics, Vol 20, Iss 1, Pp 1-8 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1080/09728600.2022.2158051","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2158051","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.8199999928474426}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1984228559","https://openalex.org/W2011039300","https://openalex.org/W2028333952","https://openalex.org/W2504650782","https://openalex.org/W2536500162","https://openalex.org/W2805978690","https://openalex.org/W2973554841","https://openalex.org/W2995238793","https://openalex.org/W3043697555","https://openalex.org/W3045696633","https://openalex.org/W3093787833","https://openalex.org/W3209279701","https://openalex.org/W3213685285","https://openalex.org/W3213861259","https://openalex.org/W4214937823"],"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":{"AbstractA":[0],"quasi-total":[1,84,98,127,139,154,171],"Roman":[2,85,99,128,140,155,172],"dominating":[3],"function":[4,12,74],"(QTRD-function)":[5],"on":[6,95],"[Formula:":[7,13,102,182],"see":[8,14,103,183],"text]":[9,15,104,184],"is":[10,27,44,69,88,109,158],"a":[11,67,93,106],"such":[16],"that":[17,115,147],"(i)":[18],"every":[19],"vertex":[20,33,47],"x":[21,43],"for":[22,35,181],"which":[23,36],"f(x)":[24,61],"=":[25,38,62],"0":[26],"adjacent":[28],"to":[29,117,120,124,163],"at":[30],"least":[31],"one":[32],"v":[34],"f(v)":[37],"2,":[39],"and":[40,82],"(ii)":[41],"if":[42],"an":[45],"isolated":[46],"in":[48,122,142],"the":[49,53,70,77,83,89,110,126,136,148,153,170],"subgraph":[50],"induced":[51],"by":[52],"set":[54,79],"of":[55,66,72,80,92,105,113,138,169],"vertices":[56],"with":[57,152],"non-zero":[58],"values,":[59],"then":[60],"1.":[63],"The":[64,97],"weight":[65,91],"QTRD-function":[68,94],"sum":[71],"its":[73],"values":[75],"over":[76],"whole":[78],"vertices,":[81],"domination":[86,129],"number":[87,101,112,174],"minimum":[90,111],"G.":[96],"reinforcement":[100,141,156,173],"graph":[107],"G":[108,121],"edges":[114],"have":[116],"be":[118],"added":[119],"order":[123],"decrease":[125],"number.":[130],"In":[131],"this":[132],"paper,":[133],"we":[134],"initiate":[135],"study":[137],"graphs.":[143,165],"We":[144],"first":[145],"show":[146],"decision":[149],"problem":[150,157],"associated":[151],"NP-hard":[159],"even":[160],"when":[161],"restricted":[162],"bipartite":[164],"Then":[166],"basic":[167],"properties":[168],"are":[175,185],"provided.":[176],"Finally,":[177],"some":[178],"sharp":[179],"bounds":[180],"also":[186],"presented.":[187]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
