{"id":"https://openalex.org/W4205243275","doi":"https://doi.org/10.1051/ro/2022005","title":"Strong equality of Roman and perfect Roman Domination in trees","display_name":"Strong equality of Roman and perfect Roman Domination in trees","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4205243275","doi":"https://doi.org/10.1051/ro/2022005"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2022005","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022005","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro200336.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro200336.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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 510006, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062707037","display_name":"Saeed Kosari","orcid":"https://orcid.org/0000-0002-1427-5473"},"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":"Saeed Kosari","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038731437","display_name":"Hadi Rahbani","orcid":"https://orcid.org/0000-0001-8580-4443"},"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":"Hadi Rahbani","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":"middle","author":{"id":"https://openalex.org/A5067587978","display_name":"Mehdi Sharifzadeh","orcid":"https://orcid.org/0000-0002-9046-9771"},"institutions":[{"id":"https://openalex.org/I3121641575","display_name":"Yasouj University","ror":"https://ror.org/05sy5hm57","country_code":"IR","type":"education","lineage":["https://openalex.org/I3121641575"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mehdi Sharifzadeh","raw_affiliation_strings":["Department of Mathematics, Yasouj University, Yasouj, Iran"],"raw_orcid":"https://orcid.org/0000-0002-9046-9771","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yasouj University, Yasouj, Iran","institution_ids":["https://openalex.org/I3121641575"]}]},{"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":"https://orcid.org/0000-0003-2298-4744","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":null,"apc_paid":null,"fwci":0.7184,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7116952,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"56","issue":"1","first_page":"381","last_page":"394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9573000073432922,"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":0.8366589546203613},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7370637059211731},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7095516324043274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6937645673751831},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6022804379463196},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5322551131248474},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4513702094554901},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4508119821548462},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08070337772369385}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8366589546203613},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7370637059211731},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7095516324043274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6937645673751831},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6022804379463196},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5322551131248474},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4513702094554901},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4508119821548462},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08070337772369385},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ro/2022005","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022005","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro200336.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:edpsciences.org:dkey/10.1051/ro/2022005","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1051/ro/2022005","raw_type":"Text"},{"id":"pmh:oai:numdam.org:RO_2022__56_1_381_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2022005/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1051/ro/2022005","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2022005","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro200336.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1560602739","display_name":null,"funder_award_id":"2021A1515011940","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G5657167529","display_name":null,"funder_award_id":"62172116","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4205243275.pdf","grobid_xml":"https://content.openalex.org/works/W4205243275.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1984228559","https://openalex.org/W2073250258","https://openalex.org/W2087928776","https://openalex.org/W2242715086","https://openalex.org/W2278299270","https://openalex.org/W2770344522","https://openalex.org/W3034951309","https://openalex.org/W3040166193","https://openalex.org/W3043697555","https://openalex.org/W3093787833","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/W2104859703","https://openalex.org/W72870998","https://openalex.org/W2763279932","https://openalex.org/W2339280209","https://openalex.org/W2346500824","https://openalex.org/W2790637388"],"abstract_inverted_index":{"A":[0],"Roman":[1,57,67,99,121],"dominating":[2,58,68,122],"function":[3,17,59,69,123],"(RD-function)":[4],"on":[5,124,159],"a":[6,16,62,165,174,200],"graph":[7,63,176],"G":[8,64,105,112,125,134,141,149,154,160,177,189,194],"=":[9,38,54,80,95,191],"(":[10,35,51,77,92,104,107,111,133,140,148,153,188,193,210,215],"V":[11,20],",":[12,178],"E":[13],")":[14,37,53,79,94,106,135,150,190,195,212],"is":[15,40,65,82,114,164,180],"f":[18,34,50,60,76,91],":":[19],"\u2192":[21],"{0,":[22],"1,":[23],"2}":[24],"satisfying":[25],"the":[26,115],"condition":[27],"that":[28,129,172],"every":[29,72,157],"vertex":[30,46,73,87],"u":[31,36,74,78],"for":[32,48,89,173],"which":[33,49,90],"0":[39,81],"adjacent":[41,83],"to":[42,84,182],"at":[43],"least":[44],"one":[45,86],"v":[47,52,88,93],"2.":[55,96],"An":[56],"in":[61],"perfect":[66],"(PRD-function)":[70],"if":[71,156],"with":[75,206],"exactly":[85],"The":[97],"(perfect)":[98,120],"domination":[100],"number":[101],"\u03b3":[102,108,130,138,145,185,207],"R":[103,110,132,139,147,187,209],"p":[109,131,146,186,208],"))":[113],"minimum":[116,162],"weight":[117,163],"of":[118,161,203],"an":[119],".":[126],"We":[127],"say":[128],"strongly":[136],"equals":[137],"),":[142,155],"denoted":[143],"by":[144],"\u2261":[151,213],"\u03b3R":[152,192,214],"RD-function":[158],"PRD-function.":[166],"In":[167],"this":[168],"paper":[169],"we":[170,198],"show":[171],"given":[175],"it":[179],"NP-hard":[181],"decide":[183],"whether":[184],"and":[196],"also":[197],"provide":[199],"constructive":[201],"characterization":[202],"trees":[204],"T":[205,211,216],").":[217]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}
