{"id":"https://openalex.org/W7204621372","doi":"https://doi.org/10.1142/s1793830926500874","title":"Secure point set domination and rigid secure point set domination in graphs","display_name":"Secure point set domination and rigid secure point set domination in graphs","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204621372","doi":"https://doi.org/10.1142/s1793830926500874"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830926500874","doi":"https://doi.org/10.1142/s1793830926500874","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830926500874","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,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-2"],"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"},"volume":null,"type":"article","is_traditional":true,"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/A5101722164","display_name":"R. Sumathi","orcid":"https://orcid.org/0009-0004-5932-594X","observed_orcids":["https://orcid.org/0009-0004-5932-594X","https://orcid.org/0000-0002-1452-736X"]},"institutions":[{"id":"https://openalex.org/I4405265996","display_name":"Mannar Thirumalai Naicker College","ror":"https://ror.org/03std5j79","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405265996"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"R. Sumathi","raw_affiliation_strings":["PG and Research Department of Mathematics, Mannar Thirumalai Naicker College (Affiliated to Maduari Kamraj University), Madurai, Tamil Nadu, India","Saraswathi Narayanan College, Madurai, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0009-0004-5932-594X","affiliations":[{"raw_affiliation_string":"PG and Research Department of Mathematics, Mannar Thirumalai Naicker College (Affiliated to Maduari Kamraj University), Madurai, Tamil Nadu, India","institution_ids":["https://openalex.org/I4405265996"]},{"raw_affiliation_string":"Saraswathi Narayanan College, Madurai, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028784193","display_name":"K. Angaleeswari","orcid":"https://orcid.org/0000-0002-6736-770X","observed_orcids":["https://orcid.org/0000-0002-6736-770X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Angaleeswari","raw_affiliation_strings":["Department of Mathematics, Saraswathi Narayanan College, Madurai, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0002-6736-770X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Saraswathi Narayanan College, Madurai, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058208182","display_name":"R. Sundareswaran","orcid":"https://orcid.org/0000-0002-0439-695X","observed_orcids":["https://orcid.org/0000-0002-0439-695X"]},"institutions":[{"id":"https://openalex.org/I1330855593","display_name":"Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology","ror":"https://ror.org/05bc5bx80","country_code":"IN","type":"education","lineage":["https://openalex.org/I1330855593"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"R. Sundareswaran","raw_affiliation_strings":["Department of Mathematics, Research Park, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Avadi, Chennai, India"],"raw_orcid":"https://orcid.org/0000-0002-0439-695X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Research Park, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Avadi, Chennai, India","institution_ids":["https://openalex.org/I1330855593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125769819","display_name":"V. Swaminathan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Swaminathan","raw_affiliation_strings":["Ramanujan Research Center in Mathematics, Saraswathi Narayanan College, Madurai, India"],"raw_orcid":"https://orcid.org/0000-0002-5840-2040","affiliations":[{"raw_affiliation_string":"Ramanujan Research Center in Mathematics, Saraswathi Narayanan College, Madurai, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9945999979972839,"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":0.9945999979972839,"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":0.004900000058114529,"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":9.999999747378752e-05,"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/dominating-sets","display_name":"dominating sets","score":0.8679999709129333},{"id":"https://openalex.org/keywords/graph-domination-parameters","display_name":"graph domination parameters","score":0.6909999847412109}],"concepts":[{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.8776000142097473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7113999724388123},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6676999926567078},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5946999788284302},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5774999856948853},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.5724999904632568},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.52920001745224},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.504800021648407},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46059998869895935},{"id":"https://openalex.org/C37810922","wikidata":"https://www.wikidata.org/wiki/Q5161409","display_name":"Connected dominating set","level":3,"score":0.3190999925136566},{"id":"https://openalex.org/C102565666","wikidata":"https://www.wikidata.org/wiki/Q1378301","display_name":"Universal set","level":3,"score":0.31189998984336853},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.2948000133037567},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.2849000096321106},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.2831999957561493},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2621999979019165}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830926500874","doi":"https://doi.org/10.1142/s1793830926500874","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830926500874","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,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-2"],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7071111778","https://openalex.org/W2612188694","https://openalex.org/W7139060847","https://openalex.org/W1791850219","https://openalex.org/W4312538974","https://openalex.org/W248890345","https://openalex.org/W7216806104","https://openalex.org/W2513388465","https://openalex.org/W4311711422","https://openalex.org/W4415915903"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,11,20,24,29,34,42,49,59,66,71,79],"see":[2,12,21,25,30,35,43,50,60,67,72,80],"text]":[3,13,22,26,31,36,44,51,61,68,73,81],"be":[4],"a":[5,38,64,75,112],"simple":[6],"graph.":[7],"A":[8,46],"dominating":[9,39,47,76],"set":[10,40,48,77,96,104,119,141],"is":[14,37,52,74],"called":[15,53],"secure":[16,55,94,102,117],"if":[17,56],"for":[18,57,108,115],"any":[19,58],"in":[23,127,143],"there":[27,62],"exists":[28,63],"such":[32,69],"that":[33,70],"of":[41,78,111],"[4].":[45],"rigid":[54,101],"unique":[65],"In":[82],"this":[83,128],"paper,":[84],"we":[85],"introduce":[86],"and":[87,99,137],"investigate":[88],"two":[89],"new":[90],"parameters,":[91],"namely,":[92],"the":[93,100,109,116],"point":[95,103,118,140],"domination":[97,105,120,142],"number":[98,121],"number.":[106],"Furthermore,":[107],"Mycielskian":[110],"graph,":[113],"bounds":[114],"are":[122,130],"established.":[123],"The":[124],"results":[125],"presented":[126],"paper":[129],"different":[131],"from":[132],"those":[133],"reported":[134],"by":[135],"Gupta":[136],"Goyal":[138],"[Secure":[139],"graphs,":[144],"TWMS":[145],"J.":[146],"Appl.":[147],"Eng.":[148],"Math.":[149],"14(2)":[150],"(2024)":[151],"605\u2013617].":[152]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-30T00:00:00"}