{"id":"https://openalex.org/W2003008424","doi":"https://doi.org/10.1142/s1793830912500061","title":"SIGNED TOTAL {K}-DOMINATION AND {K}-DOMATIC NUMBERS OF GRAPHS","display_name":"SIGNED TOTAL {K}-DOMINATION AND {K}-DOMATIC NUMBERS OF GRAPHS","publication_year":2012,"publication_date":"2012-03-01","ids":{"openalex":"https://openalex.org/W2003008424","doi":"https://doi.org/10.1142/s1793830912500061","mag":"2003008424"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500061","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500061","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/A5023197041","display_name":"Seyed Mahmoud Sheikholeslami","orcid":"https://orcid.org/0000-0003-2298-4744"},"institutions":[{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"S. M. SHEIKHOLESLAMI","raw_affiliation_strings":["Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran","institution_ids":["https://openalex.org/I51301133"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033436622","display_name":"L. Volkmann","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"L. VOLKMANN","raw_affiliation_strings":["Lehrstuhl II fuer Mathematik, RWTH Aachen University, 52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl II fuer Mathematik, RWTH Aachen University, 52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023197041"],"corresponding_institution_ids":["https://openalex.org/I51301133"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08833448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"04","issue":"01","first_page":"1250006","last_page":"1250006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9897000193595886,"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/T11476","display_name":"Graph theory and applications","score":0.9314000010490417,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/combinatorics","display_name":"Combinatorics","score":0.8450109958648682},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8245382308959961},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6644486784934998},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.5385218262672424},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5158304572105408},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.5129777789115906},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4392586946487427},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4036206007003784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04378810524940491}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8450109958648682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8245382308959961},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6644486784934998},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.5385218262672424},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5158304572105408},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.5129777789115906},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4392586946487427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4036206007003784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04378810524940491},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1793830912500061","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500061","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"},{"id":"pmh:oai:publications.rwth-aachen.de:232943","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/232943","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete mathematics 4(1), 1250006 (2012). doi:10.1142/S1793830912500061","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1543322965","https://openalex.org/W2049313845","https://openalex.org/W2057180123","https://openalex.org/W2064756224","https://openalex.org/W3141776272"],"related_works":["https://openalex.org/W2794522194","https://openalex.org/W2963404550","https://openalex.org/W30750922","https://openalex.org/W2033190383","https://openalex.org/W4299822763","https://openalex.org/W4235356280","https://openalex.org/W2339280209","https://openalex.org/W2763279932","https://openalex.org/W2612157706","https://openalex.org/W4283726592"],"abstract_inverted_index":{"Let":[0],"k":[1,39],"be":[2,9],"a":[3,10,29,77,92],"positive":[4],"integer,":[5],"and":[6,141],"let":[7],"G":[8,64,98],"simple":[11],"graph":[12],"with":[13,65],"vertex":[14,42],"set":[15,47],"V(G).":[16,45],"A":[17,46],"function":[18,33],"f":[19,51,55],":":[20],"V(G)":[21],"\u2192":[22],"{\u00b11,":[23],"\u00b12,":[24],"\u2026,":[25,54],"\u00b1k}":[26],"is":[27,75,99,117],"called":[28,76],"signed":[30,59,78,93,101,120,135,175],"total":[31,60,79,94,102,121,136,176],"{k}-dominating":[32,61,80,95],"if":[34],"\u2211":[35],"u\u2208N(v)":[36],"f(u)":[37],"\u2265":[38],"for":[40,72,148,159],"each":[41,73],"v":[43],"\u2208":[44],"{f":[48],"1":[49],",":[50,53],"2":[52],"d":[56,124],"}":[57],"of":[58,89,105,134,162,165,170,173],"functions":[62,90],"on":[63,84,97],"the":[66,100,118,132,174],"property":[67],"that":[68,113],"[Formula:":[69,109,114,149,156],"see":[70,110,115,150,157],"text]":[71,116,158],"v\u2208V(G),":[74],"family":[81,96],"(of":[82],"functions)":[83],"G.":[85],"The":[86],"maximum":[87],"number":[88,104,123],"in":[91,139],"{k}-domatic":[103],"G,":[106],"denoted":[107],"by":[108],"text].":[111,151],"Note":[112],"classical":[119],"domatic":[122,177],"S":[125],"(G).":[126],"In":[127,152],"this":[128],"paper,":[129],"we":[130,142,154],"initiate":[131],"study":[133],"k-domatic":[137],"numbers":[138],"graphs,":[140],"present":[143],"some":[144],"sharp":[145],"upper":[146],"bounds":[147],"addition,":[153],"determine":[155],"several":[160],"classes":[161],"graphs.":[163],"Some":[164],"our":[166],"results":[167],"are":[168],"extensions":[169],"known":[171],"properties":[172],"number.":[178]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}