{"id":"https://openalex.org/W7165372270","doi":"https://doi.org/10.1007/s40314-026-03835-w","title":"Graphs with unique Grundy dominating sets","display_name":"Graphs with unique Grundy dominating sets","publication_year":2026,"publication_date":"2026-06-20","ids":{"openalex":"https://openalex.org/W7165372270","doi":"https://doi.org/10.1007/s40314-026-03835-w"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-026-03835-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-026-03835-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-026-03835-w.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s40314-026-03835-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089443562","display_name":"Bo\u0161tjan Bre\u0161ar","orcid":"https://orcid.org/0000-0001-8471-4796"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Bo\u0161tjan Bre\u0161ar","raw_affiliation_strings":["Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia","Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044816279","display_name":"Tanja Dravec","orcid":"https://orcid.org/0000-0003-0540-0938"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Tanja Dravec","raw_affiliation_strings":["Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia","Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia"],"raw_orcid":"https://orcid.org/0000-0003-0540-0938","affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044816279"],"corresponding_institution_ids":["https://openalex.org/I37696226","https://openalex.org/I4210106342"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.76742068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"10","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":0.9182999730110168,"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":0.9182999730110168,"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":0.012600000016391277,"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"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.00989999994635582,"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/dominating-set","display_name":"Dominating set","score":0.8393999934196472},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6707000136375427},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6439999938011169},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5447999835014343},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5271999835968018},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.39879998564720154}],"concepts":[{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.8393999934196472},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7797999978065491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7439000010490417},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6707000136375427},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6439999938011169},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5447999835014343},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5271999835968018},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4618000090122223},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.39879998564720154},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.37709999084472656},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.3100999891757965},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s40314-026-03835-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-026-03835-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-026-03835-w.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:d.cobiss.net/repository/si:282411011","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s40314-026-03835-w","pdf_url":null,"source":{"id":"https://openalex.org/S7407055177","display_name":"dCOBISS.SI Digital Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"COBISS-ID: 73925379","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dirros.openscience.si:IzpisGradiva.php?id=30350","is_oa":true,"landing_page_url":"https://dirros.openscience.si/Dokument.php?id=46045&dn=","pdf_url":null,"source":{"id":"https://openalex.org/S4377196363","display_name":"DiRROS repository (University of Maribor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I37696226","host_organization_name":"University of Maribor","host_organization_lineage":["https://openalex.org/I37696226"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 2238-3603","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s40314-026-03835-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-026-03835-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-026-03835-w.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5073827505111694}],"awards":[{"id":"https://openalex.org/G3894112125","display_name":"Graph theory","funder_award_id":"P1-0297","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7165372270.pdf","grobid_xml":"https://content.openalex.org/works/W7165372270.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W2001549516","https://openalex.org/W2002518435","https://openalex.org/W2014928604","https://openalex.org/W2091773003","https://openalex.org/W2099618798","https://openalex.org/W2115943606","https://openalex.org/W2141046366","https://openalex.org/W2175011670","https://openalex.org/W2283061813","https://openalex.org/W2595660128","https://openalex.org/W2795526790","https://openalex.org/W2962941527","https://openalex.org/W2963693461","https://openalex.org/W2963935981","https://openalex.org/W2964124830","https://openalex.org/W3008971715","https://openalex.org/W3011998649","https://openalex.org/W3048915501","https://openalex.org/W3121718722","https://openalex.org/W3138995934","https://openalex.org/W3154464724","https://openalex.org/W3169633435","https://openalex.org/W3197285983"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,6,10,23,27,39,74,92,97,102,117,131],"graph":[3,104,132],"G":[4,15,89,105,110,133],"consider":[5,116],"procedure":[7],"of":[8,73,88,101,148,153,161,174,178,192,207,221],"building":[9],"dominating":[11,94,99,128,190],"set":[12,75,100,191],"D":[13,20,36,68,76,91],"in":[14,25,78,130,158],"by":[16],"adding":[17],"vertices":[18],"to":[19,35,67,141,169,213],"one":[21,140,188],"at":[22],"time":[24],"such":[26],"way":[28,81],"that":[29,59,123,138,185,200],"whenever":[30],"vertex":[31,40],"x":[32,64],"is":[33,65,82,106,111,135],"added":[34,66],"there":[37,134],"exists":[38],"$$y\\in":[41],"N_G[x]$$":[42],"<mml:math":[43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[44],"<mml:mrow>":[45,52],"<mml:mi>y</mml:mi>":[46],"<mml:mo>\u2208</mml:mo>":[47],"<mml:msub>":[48],"<mml:mi>N</mml:mi>":[49],"<mml:mi>G</mml:mi>":[50],"</mml:msub>":[51],"<mml:mo>[</mml:mo>":[53],"<mml:mi>x</mml:mi>":[54],"<mml:mo>]</mml:mo>":[55],"</mml:mrow>":[56,57],"</mml:math>":[58],"becomes":[60],"dominated":[61],"only":[62,187],"after":[63],".":[69],"The":[70,209],"maximum":[71],"cardinality":[72],"obtained":[77],"the":[79,84,112,142,159,175,183,193,202,218],"described":[80],"called":[83],"Grundy":[85,93,98,127,154,179,189],"domination":[86,162,180],"number":[87],"and":[90,164,196],"set.":[95],"While":[96],"connected":[103],"not":[107],"unique":[108],"unless":[109],"trivial":[113],"graph,":[114],"we":[115,181],"natural":[118],"weaker":[119,203],"uniqueness":[120,149],"condition,":[121],"notably":[122],"for":[124,150,216],"every":[125],"two":[126],"sets":[129],"an":[136],"automorphism":[137],"maps":[139],"other.":[143],"We":[144],"investigate":[145],"both":[146],"versions":[147],"several":[151],"concepts":[152],"domination,":[155],"which":[156],"appeared":[157],"context":[160],"games":[163],"are":[165],"also":[166],"closely":[167],"related":[168],"zero":[170],"forcing.":[171],"For":[172],"each":[173],"four":[176],"variations":[177],"characterize":[182,197],"graphs":[184],"have":[186],"given":[194],"type,":[195],"those":[198],"forests":[199],"enjoy":[201],"(isomorphism":[204],"based)":[205],"condition":[206],"uniqueness.":[208],"latter":[210],"characterizations":[211],"lead":[212],"efficient":[214],"algorithms":[215],"recognizing":[217],"corresponding":[219],"classes":[220],"forests.":[222]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-06-20T00:00:00"}