{"id":"https://openalex.org/W3169963727","doi":"https://doi.org/10.3390/sym13061036","title":"From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs","display_name":"From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs","publication_year":2021,"publication_date":"2021-06-08","ids":{"openalex":"https://openalex.org/W3169963727","doi":"https://doi.org/10.3390/sym13061036","mag":"3169963727"},"language":"en","primary_location":{"id":"doi:10.3390/sym13061036","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061036","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1036/pdf?version=1623298923","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/6/1036/pdf?version=1623298923","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000212299","display_name":"Abel Cabrera Mart\u00ednez","orcid":"https://orcid.org/0000-0003-2806-4842"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Abel Cabrera Mart\u00ednez","raw_affiliation_strings":["Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain"],"raw_orcid":"https://orcid.org/0000-0003-2806-4842","affiliations":[{"raw_affiliation_string":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034667032","display_name":"Alejandro Estrada\u2010Moreno","orcid":"https://orcid.org/0000-0001-9767-2177"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Alejandro Estrada-Moreno","raw_affiliation_strings":["Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9767-2177","affiliations":[{"raw_affiliation_string":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066088171","display_name":"Juan A. Rodr\u00edguez\u2010Vel\u00e1zquez","orcid":"https://orcid.org/0000-0002-9082-7647"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan Alberto Rodr\u00edguez-Vel\u00e1zquez","raw_affiliation_strings":["Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9082-7647","affiliations":[{"raw_affiliation_string":"Departament d\u2019Enginyeria Inform\u00e0tica i Matem\u00e0tiques, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034667032"],"corresponding_institution_ids":["https://openalex.org/I55952717"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6087,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72034135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"6","first_page":"1036","last_page":"1036"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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":0.9994999766349792,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9890000224113464,"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/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.8281204700469971},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7118117213249207},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6853911876678467},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5613847970962524},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5084961652755737},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.4546854496002197},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3810906708240509},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34695759415626526},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1200176477432251}],"concepts":[{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.8281204700469971},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7118117213249207},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6853911876678467},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5613847970962524},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5084961652755737},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.4546854496002197},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3810906708240509},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34695759415626526},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1200176477432251}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13061036","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061036","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1036/pdf?version=1623298923","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8ebfceacc3314768adf3eaf381191a3d","is_oa":true,"landing_page_url":"https://doaj.org/article/8ebfceacc3314768adf3eaf381191a3d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 6, p 1036 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/6/1036/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13061036","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13061036","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061036","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1036/pdf?version=1623298923","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.44999998807907104,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3169963727.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W118344247","https://openalex.org/W174831056","https://openalex.org/W560340026","https://openalex.org/W1210625746","https://openalex.org/W1984228559","https://openalex.org/W2002269329","https://openalex.org/W2003370404","https://openalex.org/W2029105623","https://openalex.org/W2053891773","https://openalex.org/W2059179208","https://openalex.org/W2202070217","https://openalex.org/W2274606173","https://openalex.org/W2538779430","https://openalex.org/W2755053059","https://openalex.org/W2973554841","https://openalex.org/W3125552545","https://openalex.org/W3178267986","https://openalex.org/W3200681023","https://openalex.org/W4214483257","https://openalex.org/W6613291721","https://openalex.org/W6694607979"],"related_works":["https://openalex.org/W2963404550","https://openalex.org/W2794522194","https://openalex.org/W2902222102","https://openalex.org/W30750922","https://openalex.org/W4378234127","https://openalex.org/W72870998","https://openalex.org/W4299822763","https://openalex.org/W2339280209","https://openalex.org/W2763279932","https://openalex.org/W2346500824"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,17,44,54,65,89,102,114,126,181],"devoted":[3],"to":[4,20,56,67,87,104,116,129],"the":[5,8,21,40,60,79,92,108,122,134,137,141,144,148,152,156,165,170,174],"study":[6],"of":[7,12,30,36,42,50,63,83,100,112,164,172,178],"quasi-total":[9,109,123,157,175],"strong":[10,98,110,124,153,176],"differential":[11,99,111,125,177],"a":[13,18,33,37,51,162,179],"graph,":[14],"and":[15,27,75,155],"it":[16],"contribution":[19],"Special":[22],"Issue":[23],"\u201cTheoretical":[24],"computer":[25],"science":[26],"discrete":[28],"mathematics\u201d":[29],"Symmetry.":[31],"Given":[32],"vertex":[34,77,145],"x\u2208V(G)":[35],"graph":[38,131,180],"G,":[39],"neighbourhood":[41,49,62,82],"x":[43,84],"denoted":[45],"by":[46],"N(x).":[47],"The":[48,97],"set":[52,73,93],"X\u2286V(G)":[53,74],"defined":[55,66,90,103,115],"be":[57,68,105,117],"N(X)=\u22c3x\u2208XN(x),":[58],"while":[59,107],"external":[61,80],"X":[64,88,101],"Ne(X)=N(X)\u2216X.":[69],"Now,":[70],"for":[71],"every":[72,76],"x\u2208X,":[78],"private":[81],"with":[85],"respect":[86],"as":[91],"Pe(x,X)={y\u2208V(G)\u2216X:N(y)\u2229X={x}}.":[94],"Let":[95],"Xw={x\u2208X:Pe(x,X)\u2260\u2300}.":[96],"\u2202s(X)=|Ne(X)|\u2212|Xw|,":[106],"G":[113],"\u2202s*(G)=max{\u2202s(X):X\u2286V(G)andXw\u2286N(X)}.":[118],"We":[119],"show":[120,168],"that":[121,169],"closely":[127],"related":[128],"several":[130],"parameters,":[132],"including":[133],"domination":[135,139,150,159],"number,":[136,140,143,147,151],"total":[138],"2-domination":[142],"cover":[146],"semitotal":[149],"differential,":[154],"Italian":[158],"number.":[160],"As":[161],"consequence":[163],"study,":[166],"we":[167],"problem":[171],"finding":[173],"NP-hard.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}