{"id":"https://openalex.org/W4391772559","doi":"https://doi.org/10.1051/ro/2024038","title":"On maximal Roman domination in graphs: complexity and algorithms","display_name":"On maximal Roman domination in graphs: complexity and algorithms","publication_year":2024,"publication_date":"2024-02-13","ids":{"openalex":"https://openalex.org/W4391772559","doi":"https://doi.org/10.1051/ro/2024038"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024038","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024038","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230619.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":true,"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":"diamond","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230619.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/A5101557904","display_name":"Yonghao Song","orcid":"https://orcid.org/0000-0003-1700-1133"},"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":"Yonghao Song","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/A5014476053","display_name":"Qiyun Liu","orcid":"https://orcid.org/0009-0009-9545-7962"},"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":"Qiyun Liu","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/A5009874737","display_name":"Zhixing Duan","orcid":"https://orcid.org/0000-0001-9011-6653"},"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":"Zhixing Duan","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":"last","author":{"id":"https://openalex.org/A5032769891","display_name":"Huiqin Jiang","orcid":"https://orcid.org/0000-0002-3316-877X"},"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"]},{"id":"https://openalex.org/I4210167317","display_name":"Qiannan Normal College For Nationalities","ror":"https://ror.org/05szpc322","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210167317"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huiqin Jiang","raw_affiliation_strings":["Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China","School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Tuyun 558000, P.R. China"],"raw_orcid":"https://orcid.org/0000-0002-3316-877X","affiliations":[{"raw_affiliation_string":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P.R. China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Tuyun 558000, P.R. China","institution_ids":["https://openalex.org/I4210167317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2882,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52449462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"58","issue":"4","first_page":"2709","last_page":"2731"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9902999997138977,"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":0.9869999885559082,"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/computer-science","display_name":"Computer science","score":0.4511435031890869},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45113405585289},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38474440574645996},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37049493193626404}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4511435031890869},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45113405585289},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38474440574645996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37049493193626404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2024038","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024038","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230619.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":true,"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"}],"best_oa_location":{"id":"doi:10.1051/ro/2024038","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024038","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/04/ro230619.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":true,"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/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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391772559.pdf","grobid_xml":"https://content.openalex.org/works/W4391772559.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1108868487","https://openalex.org/W1484040084","https://openalex.org/W1984228559","https://openalex.org/W2026300475","https://openalex.org/W2058460385","https://openalex.org/W2058946695","https://openalex.org/W2320924352","https://openalex.org/W2337802335","https://openalex.org/W2474076680","https://openalex.org/W2595550610","https://openalex.org/W2767964623","https://openalex.org/W2898860148","https://openalex.org/W2967821251","https://openalex.org/W3016425788","https://openalex.org/W3043697555","https://openalex.org/W4214937823"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"For":[0,40],"a":[1,12,21,58,90,101],"simple":[2],"undirected":[3],"connected":[4],"graph":[5],"G":[6,19,27,94,142,157,165,178,185,195],"=":[7,54,72,86,132,159],"(":[8,26,37,51,63,69,74,83,111,119,129,156,164,168,184],"V,":[9],"E":[10],"),":[11,170,186],"maximal":[13,173,206,223,234,256],"Roman":[14,174,207,224,235,257],"dominating":[15,91],"function":[16,22,148],"(MRDF)":[17],"of":[18,93,138,141,146,177,191,194,204,210,227,260],"is":[20,88,143,187,239],"f":[23,50,68,110,128,155,167],":":[24],"V":[25,48,108,126,163],")":[28,39,53,65,71,76,85,113,121,131,158,166],"\u2192":[29],"{0,":[30],"1,":[31],"2}":[32],"with":[33],"the":[34,144,172,188,205,222,255],"following":[35],"properties:":[36],"i":[38],"every":[41],"vertex":[42,59,102],"v":[43,46,52,64,80,84,103,106,112,120,161,169],"\u2208":[44,47,61,81,104,107,125,162],"{":[45,79,105,123],"|":[49,109,127],"0},":[55],"there":[56,99],"exists":[57,100],"u":[60,70,124,130],"N":[62,118],"such":[66,116],"that":[67,117,233],"2.":[73],"ii":[75],"The":[77,136],"set":[78,92],"V|f":[82],"0}":[87,115,133],"not":[89],";":[95],"In":[96,197],"other":[97],"words,":[98],"\u2260":[114],"\u2229":[122],"\u2205":[134],".":[135,196],"weight":[137,190],"an":[139,192,215],"MRDF":[140,193],"sum":[145],"its":[147],"values":[149],"over":[150],"all":[151],"vertices,":[152],"denoted":[153,180],"as":[154],"\u2211":[160],"and":[171,248,264],"domination":[175,208,225,236,258],"number":[176,209,226,259],",":[179],"by":[181],"\u03b3":[182],"mR":[183],"minimum":[189],"this":[198],"paper,":[199],"we":[200,213,231,253],"establish":[201],"some":[202],"bounds":[203],"graphs.":[211,251],"Additionally,":[212],"develop":[214],"integer":[216],"linear":[217,271],"programming":[218],"formulation":[219],"to":[220,243],"compute":[221],"any":[228],"graph.":[229],"Furthermore,":[230],"prove":[232],"problem":[237],"(MRD)":[238],"NP-complete":[240],"even":[241],"restricted":[242],"star":[244],"convex":[245],"bipartite":[246,250],"graphs":[247,266],"chordal":[249],"Lastly,":[252],"show":[254],"threshold":[261],"graphs,":[262],"trees,":[263],"block":[265],"can":[267],"be":[268],"computed":[269],"in":[270],"time.":[272]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}