{"id":"https://openalex.org/W2882985849","doi":"https://doi.org/10.3934/mfc.2018011","title":"Total <inline-formula><tex-math id=\"M1\">\\begin{document}$\\{k\\}$\\end{document}</tex-math></inline-formula>-domination in special graphs","display_name":"Total <inline-formula><tex-math id=\"M1\">\\begin{document}$\\{k\\}$\\end{document}</tex-math></inline-formula>-domination in special graphs","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2882985849","doi":"https://doi.org/10.3934/mfc.2018011","mag":"2882985849"},"language":"en","primary_location":{"id":"doi:10.3934/mfc.2018011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2018011","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=a0c2fc44-b714-4258-9d8c-2f9ceadc3c94","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=a0c2fc44-b714-4258-9d8c-2f9ceadc3c94","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067465324","display_name":"Haisheng Tan","orcid":"https://orcid.org/0000-0002-3133-1430"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haisheng Tan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028988720","display_name":"Liuyan Liu","orcid":"https://orcid.org/0009-0008-8143-3989"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liuyan Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101578956","display_name":"Hongyu Liang","orcid":"https://orcid.org/0000-0002-8149-1563"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongyu Liang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":",Facebook Seattle, 1101 Dexter Ave N, Seattle, WA 98109, USA","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":",Facebook Seattle, 1101 Dexter Ave N, Seattle, WA 98109, USA","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":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.11803292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"1","issue":"3","first_page":"255","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9886999726295471,"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":0.9886999726295471,"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/combinatorics","display_name":"Combinatorics","score":0.7878016233444214},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7695314288139343},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6250508427619934},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6248863339424133},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5215608477592468},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4619256854057312},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3354373574256897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07138416171073914},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.055653899908065796}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7878016233444214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7695314288139343},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6250508427619934},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6248863339424133},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5215608477592468},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4619256854057312},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3354373574256897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07138416171073914},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.055653899908065796},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/mfc.2018011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2018011","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=a0c2fc44-b714-4258-9d8c-2f9ceadc3c94","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/mfc.2018011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2018011","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=a0c2fc44-b714-4258-9d8c-2f9ceadc3c94","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4291318508","https://openalex.org/W2794522194","https://openalex.org/W2367715758","https://openalex.org/W2963404550","https://openalex.org/W9910182","https://openalex.org/W2349109195","https://openalex.org/W2069797780","https://openalex.org/W4297965885","https://openalex.org/W2078360221","https://openalex.org/W1983442375"],"abstract_inverted_index":{"For":[0],"a":[1,6,11,18,60],"positive":[2],"integer":[3],"$k$":[4],"and":[5,96],"graph":[7],"$G":[8],"=":[9],"(V,E)$,":[10],"function":[12,21,63],"$f:V":[13],"\\to":[14],"\\{0,1,...,k\\}$":[15],"is":[16,34,55,70],"called":[17],"total":[19,42,61,83],"$\\{k\\}$-dominating":[20,62],"of":[22,37,45,59,68,81,90],"$G$":[23],"if":[24],"$\\sum_{u\u2208":[25],"N_G(v)}f(u)\u2265":[26],"k$":[27],"for":[28,86],"each":[29],"$v\u2208":[30],"V$,":[31],"where":[32,65],"$N_G(v)$":[33],"the":[35,56,66,78,82],"neighborhood":[36],"$v$":[38],"in":[39],"$G$.":[40],"The":[41],"$\\{k\\}$-domination":[43,84],"number":[44,85],"$G$,":[46,64],"denoted":[47],"by":[48],"$\\gamma":[49],"_t^{\\left\\{":[50],"k":[51],"\\right\\}}\\left(":[52],"G":[53],"\\right)$,":[54],"minimum":[57],"weight":[58,67],"$f$":[69],"$\\sum_{v\u2208":[71],"V}f(v)$.":[72],"In":[73],"this":[74],"paper,":[75],"we":[76],"determine":[77],"exact":[79],"values":[80],"several":[87],"commonly-encountered":[88],"classes":[89],"graphs":[91],"including":[92],"cycles,":[93],"paths,":[94],"wheels,":[95],"pans.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-05-19T21:40:30.786675","created_date":"2025-10-10T00:00:00"}