{"id":"https://openalex.org/W2972467748","doi":"https://doi.org/10.1142/s1793830919500654","title":"Some results for the two disjoint connected dominating sets problem","display_name":"Some results for the two disjoint connected dominating sets problem","publication_year":2019,"publication_date":"2019-09-09","ids":{"openalex":"https://openalex.org/W2972467748","doi":"https://doi.org/10.1142/s1793830919500654","mag":"2972467748"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830919500654","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500654","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102751017","display_name":"Xianliang Liu","orcid":"https://orcid.org/0000-0003-3970-1798"},"institutions":[{"id":"https://openalex.org/I59649739","display_name":"Jiangxi University of Finance and Economics","ror":"https://ror.org/03efmyj29","country_code":"CN","type":"education","lineage":["https://openalex.org/I59649739"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianliang Liu","raw_affiliation_strings":["College of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-3970-1798","affiliations":[{"raw_affiliation_string":"College of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, P. R. China","institution_ids":["https://openalex.org/I59649739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016199317","display_name":"Zishen Yang","orcid":"https://orcid.org/0009-0001-6757-2391"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zishen Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, P. R. China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100391684","display_name":"Wei Wang","orcid":"https://orcid.org/0000-0001-6257-6564"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, P. R. China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102751017"],"corresponding_institution_ids":["https://openalex.org/I59649739"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14336349,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"06","first_page":"1950065","last_page":"1950065"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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":0.9994999766349792,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9898999929428101,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7600874900817871},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5598978400230408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5531752705574036},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5400851964950562},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.5152233242988586},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4644795358181},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.42959529161453247},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.42721980810165405},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2905086874961853},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.25002121925354004}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7600874900817871},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5598978400230408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5531752705574036},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5400851964950562},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.5152233242988586},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4644795358181},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.42959529161453247},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.42721980810165405},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2905086874961853},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.25002121925354004}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830919500654","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500654","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4490137204","display_name":null,"funder_award_id":"11701236","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1556223867","https://openalex.org/W1592922472","https://openalex.org/W1987990114","https://openalex.org/W1994188228","https://openalex.org/W2004006664","https://openalex.org/W2011039300","https://openalex.org/W2022082910","https://openalex.org/W2042626642","https://openalex.org/W2047723482","https://openalex.org/W2093381928","https://openalex.org/W2807979137","https://openalex.org/W3141863997"],"related_works":["https://openalex.org/W4313216298","https://openalex.org/W2071797893","https://openalex.org/W2097063382","https://openalex.org/W2384431448","https://openalex.org/W3002741190","https://openalex.org/W3037640829","https://openalex.org/W2893201198","https://openalex.org/W2884117239","https://openalex.org/W3189256254","https://openalex.org/W2055455751"],"abstract_inverted_index":{"As":[0],"a":[1,28,60,88,108,112,126,133,137,151,158,161],"variant":[2],"of":[3,62,87,100,170],"minimum":[4,52],"connected":[5,11,29,89,152],"dominating":[6,12],"set":[7,83],"problem,":[8],"two":[9,22,65,98],"disjoint":[10,145],"sets":[13],"(DCDS)":[14],"problem":[15,67],"is":[16,68,73,106,118,136,157,176],"to":[17,46,124],"ask":[18],"whether":[19],"there":[20,140],"are":[21,141],"DCDS":[23,66,99,109,127,138,159],"[Formula:":[24,31,35,39,84,91,101,154,167,173],"see":[25,32,36,40,85,92,102,155,168,174],"text]":[26,33,37,86,93,156,169,175],"in":[27,147],"graph":[30,58,90,123,135,153],"with":[34,51],"and":[38,42],"text],":[41,103],"if":[43,80,132,150],"not,":[44],"how":[45],"add":[47],"an":[48],"edge":[49],"subset":[50],"cardinality":[53],"such":[54],"that":[55,71],"the":[56,81,171],"new":[57],"has":[59],"pair":[61],"DCDS.":[63],"The":[64],"so":[69],"hard":[70],"it":[72,105],"NP-hard":[74],"on":[75],"trees.":[76],"In":[77],"this":[78],"paper,":[79],"vertex":[82],"can":[94],"be":[95,125,130],"partitioned":[96],"into":[97],"then":[104],"called":[107],"graph.":[110,128],"First,":[111],"necessary":[113],"but":[114,163],"not":[115],"sufficient":[116],"condition":[117],"proposed":[119],"for":[120],"cubic":[121,134],"(3-regular)":[122],"To":[129],"exact,":[131],"graph,":[139,160],"at":[142],"most":[143],"four":[144],"triangles":[146],"it.":[148],"Next,":[149],"simple":[162],"nontrivial":[164],"upper":[165],"bound":[166],"girth":[172],"presented.":[177]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}