{"id":"https://openalex.org/W2901755830","doi":"https://doi.org/10.1109/access.2018.2883028","title":"Independent Roman Domination Stable and Vertex-Critical Graphs","display_name":"Independent Roman Domination Stable and Vertex-Critical Graphs","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2901755830","doi":"https://doi.org/10.1109/access.2018.2883028","mag":"2901755830"},"language":"en","primary_location":{"id":"doi:10.1109/access.2018.2883028","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2883028","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2018.2883028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014510022","display_name":"Pu Wu","orcid":"https://orcid.org/0000-0002-1179-5748"},"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":"Pu Wu","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012636371","display_name":"Zehui Shao","orcid":"https://orcid.org/0000-0003-0764-4135"},"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":"Zehui Shao","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-0764-4135","affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004232829","display_name":"Enqiang Zhu","orcid":"https://orcid.org/0000-0002-5245-7905"},"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":"Enqiang Zhu","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032769891","display_name":"Huiqin Jiang","orcid":"https://orcid.org/0000-0002-3316-877X"},"institutions":[{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huiqin Jiang","raw_affiliation_strings":["School of Information Science and Engineering, Chengdu University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Chengdu University, Chengdu, China","institution_ids":["https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038430235","display_name":"S. Nazari-Moghaddam","orcid":"https://orcid.org/0000-0002-4955-7227"},"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. Nazari-Moghaddam","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran","institution_ids":["https://openalex.org/I51301133"]}]},{"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, Iran"],"raw_orcid":null,"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":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.18050558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"6","issue":null,"first_page":"74737","last_page":"74746"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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":0.9991999864578247,"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":0.995199978351593,"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":0.9819999933242798,"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/notation","display_name":"Notation","score":0.6904263496398926},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5952274203300476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49527302384376526},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4341372549533844},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4223301410675049},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32440197467803955},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10844123363494873}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6904263496398926},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5952274203300476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49527302384376526},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4341372549533844},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4223301410675049},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32440197467803955},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10844123363494873}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2018.2883028","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2883028","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8e1ea457ab904da8aebb52da84ee322a","is_oa":true,"landing_page_url":"https://doaj.org/article/8e1ea457ab904da8aebb52da84ee322a","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":"IEEE Access, Vol 6, Pp 74737-74746 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2018.2883028","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2883028","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G8405684219","display_name":null,"funder_award_id":"2018A0303130115","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1493071618","https://openalex.org/W1581552469","https://openalex.org/W1984228559","https://openalex.org/W1999667176","https://openalex.org/W2019578481","https://openalex.org/W2026300475","https://openalex.org/W2028111792","https://openalex.org/W2045251507","https://openalex.org/W2058946695","https://openalex.org/W2077326803","https://openalex.org/W2077686450","https://openalex.org/W2087928776","https://openalex.org/W2117222483","https://openalex.org/W2122232142","https://openalex.org/W2231408977","https://openalex.org/W2322463788","https://openalex.org/W2344417619","https://openalex.org/W2412570126","https://openalex.org/W2616042493","https://openalex.org/W2617452118","https://openalex.org/W2740775687","https://openalex.org/W4251005761","https://openalex.org/W6742121470"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2504004674","https://openalex.org/W1987679298","https://openalex.org/W2963177394","https://openalex.org/W4313359513","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W3111310291"],"abstract_inverted_index":{"ARoman":[0],"dominating":[1,58],"function(RDF)":[2],"on":[3,45,76,138],"a":[4,6,21,46,77],"graph$G$is":[5,47,78,88,108],"function$f:":[7],"V(G)":[8],"\\rightarrow":[9],"\\{0,":[10],"1,":[11],"2\\}$for":[12],"which":[13],"every":[14],"vertex":[15,22,114,152],"assigned":[16,23],"0":[17],"is":[18,30,84],"adjacent":[19],"to":[20,110],"2.":[24],"The":[25,39,70],"weight":[26,41,72],"of":[27,42,73,104,141],"an":[28,43,55,67,74],"RDF":[29,44],"the":[31,62,94,139,149],"value$\\omega":[32],"(f)":[33],"=":[34],"\\sum":[35],"_{u":[36],"\\in":[37],"V(G)}f(u)$.":[38],"minimum":[40,71],"called":[48,54,79],"theRoman":[49],"domination":[50,82,91,97,113,130],"numberof$G$.":[51],"An":[52],"RDF$f$is":[53],"independent":[56,68,89,95,128,142],"Roman":[57,81,90,96,112,129,143],"function":[59],"(IRDF)":[60],"if":[61,93,117],"set$\\{v\\in":[63],"V\\mid":[64],"f(v)\\ge":[65],"1\\}$is":[66],"set.":[69],"IRDF":[75],"theindependent":[80],"numberof$G$and":[83],"denoted":[85],"by$i_{R}(G)$.":[86],"A":[87,107],"stable":[92,131,144],"number":[98],"of$G$does":[99],"not":[100],"change":[101],"under":[102],"removal":[103],"any":[105,119],"vertex.":[106],"said":[109],"beindependent":[111],"criticalor$i_{R}$-vertex":[115],"critical,":[116],"for":[118],"vertex$v$in$G$,$i_{R}(G-v)":[120],"&lt;":[121],"i_{R}(G)$.":[122],"In":[123,155],"this":[124],"paper,":[125],"we":[126,134,147,157,165],"characterize":[127],"trees":[132],"and":[133,164],"establish":[135],"upper":[136],"bounds":[137],"order":[140],"graphs.":[145,154,169],"Also,":[146],"investigate":[148],"properties":[150],"of$i_{R}$-":[151],"critical":[153,162,167],"particular,":[156],"present":[158],"some":[159],"families":[160],"of$i_{R}$-vertex":[161],"graphs":[163],"characterize$i_{R}$-vertex":[166],"block":[168]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
