{"id":"https://openalex.org/W2078021104","doi":"https://doi.org/10.1109/tpds.2014.2311794","title":"Fault-Free Hamiltonian Cycles Passing through Prescribed Edges in <formula formulatype=\"inline\"><tex Notation=\"TeX\">$k$</tex> <mathgraphic graphicformat=\"GIF\" fileref=\"zhang-ieq1-2311794.gif\"/></formula>-Ary <formula formulatype=\"inline\"><tex Notation=\"TeX\"> $n$</tex><mathgraphic graphicformat=\"GIF\" fileref=\"zhang-ieq2-2311794.gif\"/></formula>-Cubes with Faulty Edges","display_name":"Fault-Free Hamiltonian Cycles Passing through Prescribed Edges in <formula formulatype=\"inline\"><tex Notation=\"TeX\">$k$</tex> <mathgraphic graphicformat=\"GIF\" fileref=\"zhang-ieq1-2311794.gif\"/></formula>-Ary <formula formulatype=\"inline\"><tex Notation=\"TeX\"> $n$</tex><mathgraphic graphicformat=\"GIF\" fileref=\"zhang-ieq2-2311794.gif\"/></formula>-Cubes with Faulty Edges","publication_year":2014,"publication_date":"2014-03-13","ids":{"openalex":"https://openalex.org/W2078021104","doi":"https://doi.org/10.1109/tpds.2014.2311794","mag":"2078021104"},"language":"en","primary_location":{"id":"doi:10.1109/tpds.2014.2311794","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2014.2311794","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Parallel and Distributed Systems","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/A5038528725","display_name":"Shurong Zhang","orcid":"https://orcid.org/0000-0001-7734-1039"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]},{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shurong Zhang","raw_affiliation_strings":["College of Mathematics, Taiyuan University of Technology, Shanxi, P.R. China","College of Mathematics, Taiyuan University of Technology, TaiYuan, Shanxi, 030024, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics, Taiyuan University of Technology, Shanxi, P.R. China","institution_ids":["https://openalex.org/I9086337","https://openalex.org/I181877577"]},{"raw_affiliation_string":"College of Mathematics, Taiyuan University of Technology, TaiYuan, Shanxi, 030024, China","institution_ids":["https://openalex.org/I9086337"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057281614","display_name":"Xianwen Zhang","orcid":"https://orcid.org/0000-0001-5408-8683"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianwen Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Shanxi University, Shanxi, P.R. China","School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Shanxi University, Shanxi, P.R. China","institution_ids":["https://openalex.org/I181877577"]},{"raw_affiliation_string":"School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China","institution_ids":["https://openalex.org/I181877577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038528725"],"corresponding_institution_ids":["https://openalex.org/I181877577","https://openalex.org/I9086337"],"apc_list":null,"apc_paid":null,"fwci":1.3792,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.8420428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"2","first_page":"434","last_page":"443"},"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":0.9904999732971191,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9711999893188477,"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/combinatorics","display_name":"Combinatorics","score":0.4612535238265991},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4185149669647217},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40793490409851074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3997933268547058},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2607698440551758}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4612535238265991},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4185149669647217},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40793490409851074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3997933268547058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2607698440551758},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tpds.2014.2311794","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2014.2311794","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Parallel and Distributed Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324098","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1579247759","https://openalex.org/W1969525833","https://openalex.org/W1970444112","https://openalex.org/W1975829442","https://openalex.org/W1978489882","https://openalex.org/W1980811831","https://openalex.org/W1986610917","https://openalex.org/W1990269643","https://openalex.org/W2004178113","https://openalex.org/W2015385912","https://openalex.org/W2015612745","https://openalex.org/W2019413811","https://openalex.org/W2023406382","https://openalex.org/W2024863625","https://openalex.org/W2026098617","https://openalex.org/W2033562398","https://openalex.org/W2035520583","https://openalex.org/W2037350357","https://openalex.org/W2039702758","https://openalex.org/W2042456687","https://openalex.org/W2066050542","https://openalex.org/W2071194539","https://openalex.org/W2085577088","https://openalex.org/W2099952176","https://openalex.org/W2108904169","https://openalex.org/W2133982678","https://openalex.org/W2138709550","https://openalex.org/W2149789327","https://openalex.org/W2149829263","https://openalex.org/W2149945647","https://openalex.org/W2151966819","https://openalex.org/W2154874082","https://openalex.org/W2169252125","https://openalex.org/W2611093227","https://openalex.org/W4249275203","https://openalex.org/W4254910198"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"The":[0,55],"k-ary":[1,42],"n-cube":[2,43],"Q":[3,44,117],"n":[6,47,75,85,120],"k":[9,50,78,88,123],"n":[10,62],"is":[11,58],"one":[12],"of":[13,31,114,136],"the":[14,29,130,142],"most":[15],"attractive":[16],"interconnection":[17],"networks":[18],"for":[19],"parallel":[20],"and":[21,65,127,147],"distributed":[22],"systems.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27],"consider":[28],"problem":[30],"a":[32,41,107],"fault-free":[33],"hamiltonian":[34,108],"cycle":[35,109],"passing":[36,110],"through":[37,111],"prescribed":[38],"edges":[39,113],"in":[40,116],"with":[51,92],"some":[52],"faulty":[53],"edges.":[54],"following":[56],"result":[57,143],"obtained:":[59],"For":[60],"any":[61],"\u2265":[63,67],"2":[64],"k":[66],"3,":[68],"let":[69],"F":[70,91,125],"\u2282":[71,81],"E(Q":[72,82],"),":[79],"P":[80,115,134],")":[89],"\\":[90],"|P|\u2264":[93],"2n":[94,99],"-":[95,100,124],"2,":[96],"|F|":[97],"\u2264":[98],"(|P|":[101],"+":[102],"2).":[103],"Then":[104],"there":[105],"exists":[106],"all":[112],"if":[126,129],"only":[128],"subgraph":[131],"induced":[132],"by":[133,145],"consists":[135],"pairwise":[137],"vertex-disjoint":[138],"paths.":[139],"It":[140],"improves":[141],"given":[144],"Yang":[146],"Wang":[148],"[34].":[149]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}