{"id":"https://openalex.org/W2624999672","doi":"https://doi.org/10.1080/00207160.2017.1343469","title":"Total vertex-edge domination","display_name":"Total vertex-edge domination","publication_year":2017,"publication_date":"2017-06-16","ids":{"openalex":"https://openalex.org/W2624999672","doi":"https://doi.org/10.1080/00207160.2017.1343469","mag":"2624999672"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1343469","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1343469","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5005336051","display_name":"Razika Boutrig","orcid":null},"institutions":[{"id":"https://openalex.org/I3121272148","display_name":"University of Boumerdes","ror":"https://ror.org/02dveg925","country_code":"DZ","type":"education","lineage":["https://openalex.org/I3121272148"]},{"id":"https://openalex.org/I83332908","display_name":"University of Blida","ror":"https://ror.org/03g41pw14","country_code":"DZ","type":"education","lineage":["https://openalex.org/I83332908"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Razika Boutrig","raw_affiliation_strings":["Faculty of Economic Sciences and Management, University of Boumerdes, Boumerdes, Algeria","LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria"],"affiliations":[{"raw_affiliation_string":"Faculty of Economic Sciences and Management, University of Boumerdes, Boumerdes, Algeria","institution_ids":["https://openalex.org/I3121272148"]},{"raw_affiliation_string":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria","institution_ids":["https://openalex.org/I83332908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008747635","display_name":"Mustapha Chellali","orcid":"https://orcid.org/0000-0001-5231-6195"},"institutions":[{"id":"https://openalex.org/I83332908","display_name":"University of Blida","ror":"https://ror.org/03g41pw14","country_code":"DZ","type":"education","lineage":["https://openalex.org/I83332908"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Mustapha Chellali","raw_affiliation_strings":["LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria"],"affiliations":[{"raw_affiliation_string":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria","institution_ids":["https://openalex.org/I83332908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008747635"],"corresponding_institution_ids":["https://openalex.org/I83332908"],"apc_list":null,"apc_paid":null,"fwci":1.8169,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.86711508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"95","issue":"9","first_page":"1820","last_page":"1828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9635000228881836,"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":0.9635000228881836,"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/T13991","display_name":"Nuclear Receptors and Signaling","score":0.9175000190734863,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.8575795292854309},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8536040186882019},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7894190549850464},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7688533663749695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7647250890731812},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5627045631408691},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44546547532081604},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4303341507911682},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36728158593177795}],"concepts":[{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.8575795292854309},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8536040186882019},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7894190549850464},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7688533663749695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7647250890731812},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5627045631408691},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44546547532081604},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4303341507911682},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36728158593177795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1343469","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1343469","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"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/W1997787124","https://openalex.org/W2051431590","https://openalex.org/W2066561381","https://openalex.org/W2113764055","https://openalex.org/W2987736872"],"related_works":["https://openalex.org/W2794522194","https://openalex.org/W2963404550","https://openalex.org/W30750922","https://openalex.org/W2033190383","https://openalex.org/W4235356280","https://openalex.org/W4299822763","https://openalex.org/W2339280209","https://openalex.org/W2763279932","https://openalex.org/W2612157706","https://openalex.org/W4283726592"],"abstract_inverted_index":{"A":[0,26,68],"vertex":[1,50],"v":[2],"of":[3,42,51,56,60,87,92,108,174],"a":[4,30,36,57,88,131,135,160,172],"graph":[5],"G=(V,E)":[6],"is":[7,29,44,62,71,94,122,130],"said":[8,72],"to":[9,14,22,73],"ve-dominate":[10],"every":[11,19,40],"edge":[12,20,41],"incident":[13,24],"v,":[15],"as":[16,18],"well":[17],"adjacent":[21],"these":[23],"edges.":[25],"set":[27,33,59,70,91],"S\u2286V":[28],"vertex-edge":[31,64,97,110],"dominating":[32],"(or":[34],"simply,":[35],"ve-dominating":[37,58,69,90],"set)":[38],"if":[39,76,128],"E":[43],"ve-dominated":[45],"by":[46],"at":[47],"least":[48],"one":[49],"S.":[52],"The":[53,84],"minimum":[54,85],"cardinality":[55,86],"G":[61,93,165],"the":[63,95,106,116,151],"domination":[65,98],"number":[66,99,117],"\u03b3ve(G).":[67],"be":[74],"total":[75,89,96,109],"its":[77],"induced":[78],"subgraph":[79],"has":[80],"no":[81],"isolated":[82],"vertices.":[83],"\u03b3vet(G).":[100],"In":[101],"this":[102,154],"paper":[103],"we":[104,125,149,158,170],"initiate":[105],"study":[107],"domination.":[111],"We":[112],"show":[113,126],"that":[114,127,167],"determining":[115],"\u03b3vet(G)":[118],"for":[119,163],"bipartite":[120],"graphs":[121,164],"NP-complete.":[123],"Then":[124],"T":[129,177],"tree":[132],"different":[133],"from":[134],"star":[136],"with":[137,178],"order":[138],"n,":[139],"\u2113":[140],"leaves":[141],"and":[142,169],"s":[143],"support":[144],"vertices,":[145],"then":[146],"\u03b3vet(T)\u2264(n\u2212\u2113+s)/2.":[147],"Moreover,":[148],"characterize":[150],"trees":[152,176],"attaining":[153],"upper":[155],"bound.":[156],"Finally,":[157],"establish":[159],"necessary":[161],"condition":[162],"such":[166],"\u03b3vet(G)=2\u03b3ve(G)":[168],"provide":[171],"characterization":[173],"all":[175],"\u03b3vet(T)=2\u03b3ve(T).":[179]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
