{"id":"https://openalex.org/W7167207240","doi":"https://doi.org/10.1007/s10878-026-01441-4","title":"The characterizations and complexity of Roman {2}-domination number and 2-domination number in graphs","display_name":"The characterizations and complexity of Roman {2}-domination number and 2-domination number in graphs","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7167207240","doi":"https://doi.org/10.1007/s10878-026-01441-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10878-026-01441-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10878-026-01441-4","pdf_url":null,"source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","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/A5126660167","display_name":"Cai-Xia Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cai-Xia Wang","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, 730070, China","institution_ids":["https://openalex.org/I68986083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139798783","display_name":"Yu Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I165859042","display_name":"Huaibei Normal University","ror":"https://ror.org/03ek23472","country_code":"CN","type":"education","lineage":["https://openalex.org/I165859042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Huaibei Normal University, Huaibei, Anhui, 235000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huaibei Normal University, Huaibei, Anhui, 235000, China","institution_ids":["https://openalex.org/I165859042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140007281","display_name":"Ze-Peng Li","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ze-Peng Li","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050943003","display_name":"Shou\u2010Jun Xu","orcid":"https://orcid.org/0000-0002-2046-3040"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shou-Jun Xu","raw_affiliation_strings":["School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou, 730000, Gansu, China"],"raw_orcid":"https://orcid.org/0000-0002-2046-3040","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou, 730000, Gansu, China","institution_ids":["https://openalex.org/I76214153"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050943003"],"corresponding_institution_ids":["https://openalex.org/I76214153"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.83710339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"5","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":0.980400025844574,"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":0.980400025844574,"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":0.0034000000450760126,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6442000269889832},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5397999882698059},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5268999934196472},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5235999822616577},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.504800021648407},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.49619999527931213},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4016999900341034}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8345000147819519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7721999883651733},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6442000269889832},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5397999882698059},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5268999934196472},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5235999822616577},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.504800021648407},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.49619999527931213},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.489300012588501},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.40059998631477356},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.303600013256073},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.2912999987602234},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.26100000739097595}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10878-026-01441-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10878-026-01441-4","pdf_url":null,"source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3796897130","display_name":"\u56fe\u7684\u5e73\u5747\u8ddd\u79bb\u53ca\u76f8\u5173\u95ee\u9898\u7814\u7a76","funder_award_id":"11571155","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6593394889","display_name":"Murty-Simon\u731c\u60f3\u53ca(\u5168)\u63a7\u5236\u4e34\u754c\u56fe\u3001\u8fb9\u63a7\u5236\u53c2\u6570\u4e34\u754c\u56fe\u6027\u8d28\u7684\u7814\u7a76","funder_award_id":"12071194","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1557513888","https://openalex.org/W1984228559","https://openalex.org/W2058946695","https://openalex.org/W2090249824","https://openalex.org/W2202070217","https://openalex.org/W2538779430","https://openalex.org/W2734720563","https://openalex.org/W2759838277","https://openalex.org/W3033915607","https://openalex.org/W3129470409","https://openalex.org/W3157752031"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-07-04T00:00:00"}
