{"id":"https://openalex.org/W4399886989","doi":"https://doi.org/10.3390/sym16070781","title":"Bound for the k-Fault-Tolerant Power-Domination Number","display_name":"Bound for the k-Fault-Tolerant Power-Domination Number","publication_year":2024,"publication_date":"2024-06-21","ids":{"openalex":"https://openalex.org/W4399886989","doi":"https://doi.org/10.3390/sym16070781"},"language":"en","primary_location":{"id":"doi:10.3390/sym16070781","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070781","pdf_url":"https://www.mdpi.com/2073-8994/16/7/781/pdf?version=1718962508","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/2073-8994/16/7/781/pdf?version=1718962508","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041405224","display_name":"Lakshmi Girish","orcid":null},"institutions":[{"id":"https://openalex.org/I81556334","display_name":"Amrita Vishwa Vidyapeetham","ror":"https://ror.org/03am10p12","country_code":"IN","type":"education","lineage":["https://openalex.org/I81556334"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Lakshmi Girish","raw_affiliation_strings":["Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Kochi 682024, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Kochi 682024, India","institution_ids":["https://openalex.org/I81556334"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026730702","display_name":"K. Somasundaram","orcid":"https://orcid.org/0000-0003-2226-1845"},"institutions":[{"id":"https://openalex.org/I81556334","display_name":"Amrita Vishwa Vidyapeetham","ror":"https://ror.org/03am10p12","country_code":"IN","type":"education","lineage":["https://openalex.org/I81556334"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Kanagasabapathi Somasundaram","raw_affiliation_strings":["Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India"],"raw_orcid":"https://orcid.org/0000-0003-2226-1845","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India","institution_ids":["https://openalex.org/I81556334"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026730702"],"corresponding_institution_ids":["https://openalex.org/I81556334"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08610054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"7","first_page":"781","last_page":"781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9990000128746033,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9987999796867371,"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/T12326","display_name":"Network Packet Processing and Optimization","score":0.9757999777793884,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/domination-analysis","display_name":"Domination analysis","score":0.7745896577835083},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.7545751333236694},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7483779788017273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6879416704177856},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5559828877449036},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.547941267490387},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47782185673713684},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4288513660430908},{"id":"https://openalex.org/keywords/fault-tolerance","display_name":"Fault tolerance","score":0.4172680079936981},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20212695002555847},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1601879894733429},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.06634959578514099},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.051047712564468384}],"concepts":[{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7745896577835083},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.7545751333236694},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7483779788017273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6879416704177856},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5559828877449036},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.547941267490387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47782185673713684},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4288513660430908},{"id":"https://openalex.org/C63540848","wikidata":"https://www.wikidata.org/wiki/Q3140932","display_name":"Fault tolerance","level":2,"score":0.4172680079936981},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20212695002555847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1601879894733429},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.06634959578514099},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.051047712564468384},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16070781","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070781","pdf_url":"https://www.mdpi.com/2073-8994/16/7/781/pdf?version=1718962508","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:57f90fc9aaa24208873e71f3378b2fde","is_oa":false,"landing_page_url":"https://doaj.org/article/57f90fc9aaa24208873e71f3378b2fde","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 7, p 781 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16070781","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070781","pdf_url":"https://www.mdpi.com/2073-8994/16/7/781/pdf?version=1718962508","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":[{"score":0.5299999713897705,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G6611645","display_name":null,"funder_award_id":"PVO/Pubn/2024/041","funder_id":"https://openalex.org/F4320311327","funder_display_name":"Amrita Vishwa Vidyapeetham University"}],"funders":[{"id":"https://openalex.org/F4320311327","display_name":"Amrita Vishwa Vidyapeetham University","ror":"https://ror.org/03am10p12"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4399886989.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1964514587","https://openalex.org/W1991484377","https://openalex.org/W1995497993","https://openalex.org/W2003370404","https://openalex.org/W2023728975","https://openalex.org/W2156804553","https://openalex.org/W2162765501","https://openalex.org/W2981017988","https://openalex.org/W3040399125","https://openalex.org/W3088010465","https://openalex.org/W3093918819","https://openalex.org/W3129139193","https://openalex.org/W3158818916","https://openalex.org/W4281482052"],"related_works":["https://openalex.org/W2963404550","https://openalex.org/W2794522194","https://openalex.org/W2984335350","https://openalex.org/W1123717642","https://openalex.org/W3217516113","https://openalex.org/W4226354266","https://openalex.org/W2736530170","https://openalex.org/W4313020364","https://openalex.org/W2034961945","https://openalex.org/W2762120601"],"abstract_inverted_index":{"A":[0],"set":[1,10,23,45],"S\u2286V":[2],"is":[3,33,46],"referred":[4],"to":[5],"as":[6],"a":[7,12,21,42],"k-fault-tolerant":[8,43,48,75],"power-dominating":[9,22,44],"of":[11,24,41,51,78,93],"given":[13],"graph":[14,67],"G=(V,E)":[15],"if":[16],"the":[17,47,74,79,91],"difference":[18],"S\u2216F":[19],"remains":[20],"G":[25],"for":[26,90],"any":[27],"F\u2286S":[28],"with":[29,36],"|F|\u2264k,":[30],"where":[31],"k":[32],"an":[34],"integer":[35],"0\u2264k&lt;|V|.":[37],"The":[38],"lowest":[39],"cardinality":[40],"power-domination":[49,76],"number":[50,77],"G,":[52],"denoted":[53],"by":[54],"\u03b3Pk(G).":[55],"Generalized":[56],"Petersen":[57,81],"graphs":[58,82],"GP(m,k)":[59],"and":[60,84,96],"generalized":[61,80],"cylinders":[62,94],"SG":[63],"are":[64],"two":[65],"well-known":[66],"classes.":[68],"In":[69],"this":[70],"paper,":[71],"we":[72,87],"calculate":[73],"GP(m,1)":[83],"GP(m,2).":[85],"Also,":[86],"obtain":[88],"\u03b3Pk(G)":[89],"subclasses":[92],"SCm":[95],"SBm.":[97]},"counts_by_year":[],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2024-06-22T00:00:00"}
