{"id":"https://openalex.org/W4403583099","doi":"https://doi.org/10.1093/comjnl/bxae098","title":"The <i>h</i>-faulty-block connectivity of <i>k</i>-ary <i>n</i>-cubes","display_name":"The <i>h</i>-faulty-block connectivity of <i>k</i>-ary <i>n</i>-cubes","publication_year":2024,"publication_date":"2024-10-19","ids":{"openalex":"https://openalex.org/W4403583099","doi":"https://doi.org/10.1093/comjnl/bxae098"},"language":"en","primary_location":{"id":"doi:10.1093/comjnl/bxae098","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxae098","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","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/A5016236146","display_name":"Xiaohui Hua","orcid":"https://orcid.org/0000-0002-1215-3616"},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaohui Hua","raw_affiliation_strings":["School of Mathematics and Information Science, Henan Normal University , Xinxiang, Henan 453007 ,","School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Normal University , Xinxiang, Henan 453007 ,","institution_ids":["https://openalex.org/I75955062"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102771457","display_name":"Qin Zhao","orcid":"https://orcid.org/0000-0001-7579-2004"},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qin Zhao","raw_affiliation_strings":["School of Mathematics and Information Science, Henan Normal University , Xinxiang, Henan 453007 ,","School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Normal University , Xinxiang, Henan 453007 ,","institution_ids":["https://openalex.org/I75955062"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China","institution_ids":["https://openalex.org/I75955062"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016236146"],"corresponding_institution_ids":["https://openalex.org/I75955062"],"apc_list":{"value":2635,"currency":"GBP","value_usd":3232},"apc_paid":null,"fwci":0.2841,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57649154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"68","issue":"2","first_page":"126","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":1.0,"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":1.0,"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/T10847","display_name":"Advanced Optical Network Technologies","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10772","display_name":"Distributed systems and fault tolerance","score":0.9911999702453613,"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/block","display_name":"Block (permutation group theory)","score":0.6941366195678711},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5398731231689453},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.507028341293335},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3350977301597595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3260423541069031}],"concepts":[{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6941366195678711},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5398731231689453},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.507028341293335},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3350977301597595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3260423541069031}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/comjnl/bxae098","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxae098","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1971967319","https://openalex.org/W2012866905","https://openalex.org/W2029615720","https://openalex.org/W2033449646","https://openalex.org/W2039721538","https://openalex.org/W2093840292","https://openalex.org/W2109894628","https://openalex.org/W2124839136","https://openalex.org/W2125993726","https://openalex.org/W2138709550","https://openalex.org/W2149945647","https://openalex.org/W2169989080","https://openalex.org/W2338928843","https://openalex.org/W2465967402","https://openalex.org/W2516982167","https://openalex.org/W2777090724","https://openalex.org/W2904776587","https://openalex.org/W2963538553","https://openalex.org/W2964129534","https://openalex.org/W3017184626","https://openalex.org/W3024902839","https://openalex.org/W3084775690","https://openalex.org/W4239617800","https://openalex.org/W4313827789"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2029210135"],"abstract_inverted_index":{"Abstract":[0],"The":[1,125],"connectivity":[2,22],"of":[3,21,82,85,109,118,131],"a":[4,64,92,100,152],"network":[5,55,68],"is":[6,105,113,133],"an":[7,107],"important":[8],"indicator":[9],"for":[10,54,67,146,163,171,178,182,189,193,198],"assessing":[11],"its":[12],"reliability":[13],"and":[14,41,97,115,161,174,185,196,201],"fault":[15,29],"tolerability.":[16],"However,":[17],"currently":[18],"various":[19],"kinds":[20],"do":[23],"not":[24],"well":[25],"reflect":[26],"the":[27,75,83,86],"network\u2019s":[28],"tolerance":[30],"when":[31],"facing":[32],"certain":[33],"attacks":[34],"such":[35],"as":[36],"Botnet":[37],"attacks,":[38,40],"DDoS":[39],"Local":[42],"Area":[43],"Network":[44],"Denial":[45],"attacks.":[46],"Therefore,":[47],"Lin":[48],"et":[49],"al.":[50],"(A":[51],"novel":[52],"measurement":[53,66,71],"reliability.":[56,69],"IEEE":[57],"Trans":[58],"Comput":[59],"2021;":[60],"70:":[61],"17191731.)":[62],"proposed":[63],"new":[65],"This":[70],"method":[72],"can":[73],"resist":[74],"block":[76],"attack":[77],"by":[78,138],"taking":[79],"into":[80],"account":[81],"dispersity":[84],"remaining":[87],"nodes.":[88,124],"Let":[89],"$G$":[90,110,132],"be":[91,99],"network,":[93],"$C":[94],"\\subset":[95],"V(G)$,":[96],"$G[C]$":[98],"connected":[101],"subgraph.":[102],"Then":[103],"$C$":[104],"called":[106,134],"$h$-faulty-block":[108,130,135],"if":[111],"$G-C$":[112,119],"disconnected,":[114],"every":[116],"component":[117],"has":[120],"at":[121],"least":[122],"$h+1$":[123],"minimum":[126],"cardinality":[127],"over":[128],"all":[129],"connectivity,":[136],"denoted":[137],"$FB_{k_{h}}(G)$.":[139],"In":[140],"this":[141],"paper,":[142],"we":[143,167],"determine":[144],"$FB_{k_{h}}(Q_{n}^{k})$":[145],"$k$-ary":[147],"$n$-cube":[148],"$Q_{n}^{k}$":[149],"($k\\geq":[150],"3$),":[151],"classic":[153],"interconnection":[154],"network.":[155],"We":[156],"prove":[157],"that":[158,169],"$FB_{k_{0}}(Q_{n}^{3})=3n-1$,":[159],"$FB_{k_{1}}(Q_{n}^{3})=5n-4$,":[160],"$FB_{k_{2}}(Q_{n}^{3})=7n-9$":[162],"$n\\geq":[164,175,179,186,190,194,202],"3$.":[165],"Also,":[166],"show":[168],"$FB_{k_{0}}(Q_{n}^{k})=4n-1$":[170],"$k\\geq":[172,183,199],"4$":[173],"2$,":[176],"$FB_{k_{1}}(Q_{n}^{4})=6n-4$":[177],"3$,":[180,187],"$FB_{k_{1}}(Q_{n}^{k})=6n-3$":[181],"5$":[184],"$FB_{k_{2}}(Q_{n}^{4})=8n-7$":[188],"4$,":[191,195],"$FB_{k_{2}}(Q_{n}^{5})=8n-6$":[192],"$FB_{k_{2}}(Q_{n}^{k})=8n-5$":[197],"6$":[200],"5$.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}