{"id":"https://openalex.org/W7124299769","doi":"https://doi.org/10.48550/arxiv.2601.09167","title":"On the complexity of global Roman domination problem in graphs","display_name":"On the complexity of global Roman domination problem in graphs","publication_year":2026,"publication_date":"2026-01-14","ids":{"openalex":"https://openalex.org/W7124299769","doi":"https://doi.org/10.48550/arxiv.2601.09167"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.09167","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.09167","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2601.09167","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059493841","display_name":"Sangam Balchandar Reddy","orcid":"https://orcid.org/0000-0002-5848-3821"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reddy, Sangam Balchandar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123055717","display_name":"Arun Kumar Das","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Das, Arun Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055647664","display_name":"Anjeneya Swami Kare","orcid":"https://orcid.org/0000-0003-3644-4802"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kare, Anjeneya Swami","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5123137511","display_name":"I. Vinod Reddy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reddy, I. Vinod","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9800999760627747,"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":0.9800999760627747,"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":0.005200000014156103,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7595000267028809},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6128000020980835},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.6121000051498413},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5113000273704529},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49549999833106995},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.45750001072883606}],"concepts":[{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7595000267028809},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7074000239372253},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6284999847412109},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6128000020980835},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.6121000051498413},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5113000273704529},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49549999833106995},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.45750001072883606},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3368000090122223},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.31949999928474426},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.31869998574256897},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.2897999882698059}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.09167","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.09167","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2601.09167","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.09167","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0,39],"Roman":[1,40,47,54,84,92,102,109,125,141,145,172,199,230],"dominating":[2,41,48,55,93,110],"function":[3,42,49,56,94,111],"of":[4,66,71,82,100,112,123],"a":[5,9,31,45,53,90,107,225],"graph":[6,130,154],"$G=(V,E)$":[7],"is":[8,44,52,68,87,104,159,165,175,202],"labeling":[10],"$f:":[11],"V":[12],"\\rightarrow{}":[13],"\\{0":[14],",1,":[15],"2\\}$":[16],"such":[17],"that":[18,140,170,197],"for":[19,57,228],"each":[20],"vertex":[21,32],"$u":[22,77],"\\in":[23,34,78],"V$":[24],"with":[25,36,95,211],"$f(u)":[26],"=":[27],"0$,":[28],"there":[29],"exists":[30],"$v":[33],"N(u)$":[35],"$f(v)":[37],"=2$.":[38],"$f$":[43,67],"global":[46,91,108],"if":[50],"it":[51],"both":[58],"$G$":[59],"and":[60,132,143,188,215],"its":[61],"complement":[62],"$\\overline{G}$.":[63],"The":[64,80,98],"weight":[65],"the":[69,75,120,134,163,220],"sum":[70],"$f(u)$":[72],"over":[73],"all":[74],"vertices":[76],"V$.":[79],"objective":[81,99],"Global":[83,101,124,144,171,198,229],"Domination":[85,103,126,146,173,200],"problem":[86,127,174,201,232],"to":[88,105],"find":[89],"minimum":[96,113],"weight.":[97,114],"compute":[106],"In":[115],"this":[116],"paper,":[117],"we":[118,223],"study":[119],"algorithmic":[121],"aspects":[122],"on":[128,156,177,204,233],"various":[129],"classes":[131,155],"obtain":[133],"following":[135],"results.":[136],"1.":[137],"We":[138,168,195],"prove":[139,196],"domination":[142,231],"problems":[147],"are":[148],"not":[149],"computationally":[150],"equivalent":[151],"by":[152,186],"identifying":[153],"which":[157],"one":[158],"linear-time":[160,226],"solvable,":[161],"while":[162],"other":[164],"NP-complete.":[166],"2.":[167],"show":[169],"NP-complete":[176,203],"split":[178],"graphs,":[179,207],"thereby":[180],"resolving":[181],"an":[182],"open":[183],"question":[184],"posed":[185],"Panda":[187],"Goyal":[189],"[Discrete":[190],"Applied":[191],"Mathematics,":[192],"2023].":[193],"3.":[194],"chordal":[205],"bipartite":[206,209],"planar":[208],"graphs":[210],"maximum":[212],"degree":[213],"five":[214],"circle":[216],"graphs.":[217],"4.":[218],"On":[219],"positive":[221],"side,":[222],"present":[224],"algorithm":[227],"cographs.":[234]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-01-16T00:00:00"}