{"id":"https://openalex.org/W3209279701","doi":"https://doi.org/10.1080/09728600.2021.1992257","title":"On the total Roman domination stability in graphs","display_name":"On the total Roman domination stability in graphs","publication_year":2021,"publication_date":"2021-09-02","ids":{"openalex":"https://openalex.org/W3209279701","doi":"https://doi.org/10.1080/09728600.2021.1992257","mag":"3209279701"},"language":"en","primary_location":{"id":"doi:10.1080/09728600.2021.1992257","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2021.1992257","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/09728600.2021.1992257?needAccess=true","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://www.tandfonline.com/doi/pdf/10.1080/09728600.2021.1992257?needAccess=true","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025168651","display_name":"Ghazale Asemian","orcid":null},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ghazale Asemian","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047381769","display_name":"Nader Jafari Rad","orcid":"https://orcid.org/0000-0001-7406-1859"},"institutions":[{"id":"https://openalex.org/I119025939","display_name":"Shahed University","ror":"https://ror.org/01e8ff003","country_code":"IR","type":"education","lineage":["https://openalex.org/I119025939"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Nader Jafari Rad","raw_affiliation_strings":["Department of Mathematics, Shahed University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahed University, Tehran, Iran","institution_ids":["https://openalex.org/I119025939"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011236167","display_name":"Abolfazl Tehranian","orcid":"https://orcid.org/0000-0002-5811-1139"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Abolfazl Tehranian","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029496455","display_name":"H. Rasouli","orcid":"https://orcid.org/0000-0002-7115-6390"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hamid Rasouli","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047381769"],"corresponding_institution_ids":["https://openalex.org/I119025939"],"apc_list":{"value":1000,"currency":"GBP","value_usd":1226},"apc_paid":{"value":1000,"currency":"GBP","value_usd":1226},"fwci":0.2895,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62271986,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"18","issue":"3","first_page":"166","last_page":"172"},"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":0.9889000058174133,"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":0.9821000099182129,"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":0.8842237591743469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8229199051856995},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7681776285171509},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7164065837860107},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.539859414100647},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5387794375419617},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4102737307548523},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3231773376464844}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8842237591743469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8229199051856995},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7681776285171509},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7164065837860107},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.539859414100647},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5387794375419617},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4102737307548523},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3231773376464844}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/09728600.2021.1992257","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2021.1992257","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/09728600.2021.1992257?needAccess=true","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:069f0108d5194a66b09200c36a9b8653","is_oa":true,"landing_page_url":"https://doaj.org/article/069f0108d5194a66b09200c36a9b8653","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics, Vol 18, Iss 3, Pp 166-172 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1080/09728600.2021.1992257","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2021.1992257","pdf_url":"https://www.tandfonline.com/doi/pdf/10.1080/09728600.2021.1992257?needAccess=true","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":[{"display_name":"Peace, Justice and strong institutions","score":0.6800000071525574,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1493071618","https://openalex.org/W1984228559","https://openalex.org/W1991685641","https://openalex.org/W2028333952","https://openalex.org/W2040414111","https://openalex.org/W2066577300","https://openalex.org/W2341947675","https://openalex.org/W2504650782","https://openalex.org/W2774405535","https://openalex.org/W2805978690","https://openalex.org/W2964203300","https://openalex.org/W3009731148","https://openalex.org/W3043697555","https://openalex.org/W3093787833","https://openalex.org/W3101908763","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/W2033190383"],"abstract_inverted_index":{"A":[0],"total":[1,62,67,98,113],"Roman":[2,63,68,99,114],"dominating":[3],"function":[4,11],"on":[5],"a":[6,10,73,119],"graph":[7,74],"G":[8,32,75],"is":[9,23,59,82,128],"satisfying":[12],"the":[13,39,43,61,83,97,112,124],"conditions:":[14],"(i)":[15],"every":[16],"vertex":[17,29],"u":[18],"with":[19,76],"f(u)":[20],"=":[21,36],"0":[22],"adjacent":[24],"to":[25,133],"at":[26],"least":[27],"one":[28],"v":[30],"of":[31,54,72,86,102,118],"for":[33,111],"which":[34],"f(v)":[35],"2;":[37],"(ii)":[38],"subgraph":[40],"induced":[41],"by":[42,81],"vertices":[44,87,94],"assigned":[45],"non-zero":[46],"values":[47],"has":[48],"no":[49,77],"isolated":[50,78,93],"vertices.":[51],"The":[52,66],"minimum":[53,84],"over":[55],"all":[56],"such":[57],"functions":[58],"called":[60],"domination":[64,69,100,115],"number":[65,71,85,101,117],"stability":[70,116],"vertex,":[79],"denoted":[80],"whose":[88],"removal":[89],"does":[90],"not":[91],"produce":[92],"and":[95,121],"changes":[96],"G.":[103],"In":[104],"this":[105],"paper":[106],"we":[107],"present":[108],"some":[109],"bounds":[110],"graph,":[120],"prove":[122],"that":[123],"associated":[125],"decision":[126],"problem":[127],"NP-hard":[129],"even":[130],"when":[131],"restricted":[132],"bipartite":[134],"graphs":[135],"or":[136],"planar":[137],"graphs.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-19T21:40:30.786675","created_date":"2025-10-10T00:00:00"}