{"id":"https://openalex.org/W4306884838","doi":"https://doi.org/10.1142/s1793830922501725","title":"Strong restrained domination number on trees and product of graphs: An algorithmic approach","display_name":"Strong restrained domination number on trees and product of graphs: An algorithmic approach","publication_year":2022,"publication_date":"2022-10-20","ids":{"openalex":"https://openalex.org/W4306884838","doi":"https://doi.org/10.1142/s1793830922501725"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922501725","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501725","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/A5033620579","display_name":"Shanmugam Esakkimuthu","orcid":null},"institutions":[{"id":"https://openalex.org/I13268429","display_name":"Madurai Kamaraj University","ror":"https://ror.org/04c8e9019","country_code":"IN","type":"education","lineage":["https://openalex.org/I13268429"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Shanmugam Esakkimuthu","raw_affiliation_strings":["National Centre of Excellence, Thiagarajar College, Madurai Kamaraj University, Madurai 625 009, Tamilnadu, India"],"raw_orcid":"https://orcid.org/0000-0001-7840-2382","affiliations":[{"raw_affiliation_string":"National Centre of Excellence, Thiagarajar College, Madurai Kamaraj University, Madurai 625 009, Tamilnadu, India","institution_ids":["https://openalex.org/I13268429"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089478916","display_name":"Pandiaraja Duraisamy","orcid":null},"institutions":[{"id":"https://openalex.org/I13268429","display_name":"Madurai Kamaraj University","ror":"https://ror.org/04c8e9019","country_code":"IN","type":"education","lineage":["https://openalex.org/I13268429"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pandiaraja Duraisamy","raw_affiliation_strings":["National Centre of Excellence and Department of Mathematics, Thiagarajar College, Madurai Kamaraj University, Madurai 625 009, Tamilnadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre of Excellence and Department of Mathematics, Thiagarajar College, Madurai Kamaraj University, Madurai 625 009, Tamilnadu, India","institution_ids":["https://openalex.org/I13268429"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080906293","display_name":"Prabakaran Ganesan","orcid":null},"institutions":[{"id":"https://openalex.org/I13268429","display_name":"Madurai Kamaraj University","ror":"https://ror.org/04c8e9019","country_code":"IN","type":"education","lineage":["https://openalex.org/I13268429"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Prabakaran Ganesan","raw_affiliation_strings":["Department of Mathematics, Thiagarajar College, Madurai Kamaraj University, Madurai 625 009, Tamilnadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Thiagarajar College, Madurai Kamaraj University, Madurai 625 009, Tamilnadu, India","institution_ids":["https://openalex.org/I13268429"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033620579"],"corresponding_institution_ids":["https://openalex.org/I13268429"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15700105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"08","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":0.9995999932289124,"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":0.9995999932289124,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9692999720573425,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9352999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7656190395355225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7462977170944214},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7268775701522827},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.7224648594856262},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6851918697357178},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.6192516088485718},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.6062134504318237},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.508134126663208},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5061277747154236},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.49097755551338196},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.42615509033203125},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.35885143280029297},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35507553815841675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11060181260108948}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7656190395355225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7462977170944214},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7268775701522827},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7224648594856262},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6851918697357178},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.6192516088485718},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.6062134504318237},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.508134126663208},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5061277747154236},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49097755551338196},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.42615509033203125},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35885143280029297},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35507553815841675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11060181260108948},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922501725","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501725","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6724749077","display_name":null,"funder_award_id":"F. No. 5-6/2013 -TS-VII dt. 28.09.2015","funder_id":"https://openalex.org/F4320322724","funder_display_name":"Ministry of Education, India"}],"funders":[{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1519556010","https://openalex.org/W2009525588","https://openalex.org/W2067264828","https://openalex.org/W2103411036","https://openalex.org/W3099344741"],"related_works":["https://openalex.org/W2963404550","https://openalex.org/W2794522194","https://openalex.org/W2984335350","https://openalex.org/W1123717642","https://openalex.org/W2070745899","https://openalex.org/W1464226492","https://openalex.org/W2738565459","https://openalex.org/W2054696976","https://openalex.org/W2235657338","https://openalex.org/W2210663800"],"abstract_inverted_index":{"A":[0],"restrained":[1,13,42,53,113,143],"dominating":[2,14,43],"set":[3,15,44],"[Formula:":[4,21,29,33,57,65,74,81,89,93,132,147,151,156,160,165],"see":[5,22,30,34,58,66,75,82,90,94,133,148,152,157,161,166],"text]":[6,23,31,59,83,95,134,149,153,158,162,167],"is":[7,24,47,62,84,168],"said":[8,48],"to":[9,26,49],"be":[10,50],"a":[11,27,40,85],"strong":[12,41,52,112,118,142],"of":[16,39,45,56,87,116,146],"G":[17,46],"if":[18,80],"every":[19],"vertex":[20,28],"adjacent":[25],"and":[32,60,96,119,127,150,159],"text].":[35,67,76],"The":[36],"minimum":[37],"cardinality":[38],"the":[51,71,98,111,141],"domination":[54,114,144],"number":[55,115,145],"it":[61,128],"denoted":[63],"by":[64,101],"We":[68,77],"characterize":[69,97],"all":[70],"trees":[72,100],"with":[73],"show":[78],"that":[79,131],"tree":[86],"order":[88],"text],":[91],"then":[92],"extremal":[99],"achieving":[102],"this":[103],"lower":[104],"bound.":[105],"Simulation":[106],"was":[107,129],"carried":[108],"out":[109],"for":[110,154,163],"Cartesian,":[117],"lexicographic":[120],"product":[121],"under":[122,135],"four":[123,137],"different":[124],"network":[125,138],"topologies":[126],"noted":[130],"these":[136],"topologies.":[139],"Furthermore,":[140],"any":[155,164],"determined.":[169]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}