{"id":"https://openalex.org/W3032551786","doi":"https://doi.org/10.37236/9184","title":"Perfect State Transfer on Cayley Graphs over Dihedral Groups: The Non-Normal Case","display_name":"Perfect State Transfer on Cayley Graphs over Dihedral Groups: The Non-Normal Case","publication_year":2020,"publication_date":"2020-05-29","ids":{"openalex":"https://openalex.org/W3032551786","doi":"https://doi.org/10.37236/9184","mag":"3032551786"},"language":"en","primary_location":{"id":"doi:10.37236/9184","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9184","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/9184","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026635882","display_name":"Xiwang Cao","orcid":"https://orcid.org/0000-0002-6950-8588"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiwang Cao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081545653","display_name":"Bocong Chen","orcid":"https://orcid.org/0000-0001-5295-8403"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bocong Chen","raw_affiliation_strings":["South China University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"South China University of Technology","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063268716","display_name":"San Ling","orcid":"https://orcid.org/0000-0002-1978-3557"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"San Ling","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3541,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.85185587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9858999848365784,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9661999940872192,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/dihedral-group","display_name":"Dihedral group","score":0.8475373983383179},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.8332325220108032},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6363619565963745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.61968594789505},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6103922128677368},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5518655180931091},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4918670654296875},{"id":"https://openalex.org/keywords/transfer","display_name":"Transfer (computing)","score":0.4877987205982208},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4570084512233734},{"id":"https://openalex.org/keywords/non-abelian-group","display_name":"Non-abelian group","score":0.44493499398231506},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.2862185835838318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13341379165649414},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.10070744156837463},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07347625494003296},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06858804821968079}],"concepts":[{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.8475373983383179},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.8332325220108032},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6363619565963745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.61968594789505},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6103922128677368},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5518655180931091},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4918670654296875},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.4877987205982208},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4570084512233734},{"id":"https://openalex.org/C170124329","wikidata":"https://www.wikidata.org/wiki/Q592651","display_name":"Non-abelian group","level":4,"score":0.44493499398231506},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.2862185835838318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13341379165649414},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.10070744156837463},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07347625494003296},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06858804821968079},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/9184","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9184","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/147683","is_oa":true,"landing_page_url":"https://hdl.handle.net/10356/147683","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.37236/9184","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9184","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2898940288","https://openalex.org/W2378553828","https://openalex.org/W3086562803","https://openalex.org/W4385644469","https://openalex.org/W4362737391","https://openalex.org/W4226183773","https://openalex.org/W4320890122","https://openalex.org/W4315700886","https://openalex.org/W4221158338","https://openalex.org/W4286685097"],"abstract_inverted_index":{"Recently,":[0],"perfect":[1,56],"state":[2,57],"transfer":[3,58],"(PST":[4],"for":[5,49],"short)":[6],"on":[7],"graphs":[8,38,51],"has":[9,157],"attracted":[10],"great":[11],"attention":[12],"due":[13],"to":[14],"their":[15],"applications":[16],"in":[17,65,85,93,106],"quantum":[18,22],"information":[19],"processing":[20],"and":[21,26,46],"computations.":[23],"Many":[24],"constructions":[25],"results":[27],"have":[28,140],"been":[29],"established":[30],"through":[31],"various":[32],"graphs.":[33,44],"However,":[34],"most":[35],"of":[36,71,74,96,129],"the":[37,69,72,75,89,94,97,102,107,115,121,127,130],"previously":[39],"investigated":[40],"are":[41],"abelian":[42,108],"Cayley":[43,50],"Necessary":[45],"sufficient":[47],"conditions":[48],"over":[52],"dihedral":[53,131],"groups":[54],"having":[55],"were":[59],"studied":[60],"recently.":[61],"The":[62],"key":[63],"idea":[64],"that":[66,136,153],"paper":[67],"is":[68,92,144,151,161],"assumption":[70],"normality":[73],"connection":[76,90],"set.":[77],"In":[78,110,118],"those":[79],"cases,":[80],"viewed":[81],"as":[82],"an":[83],"element":[84],"a":[86],"group":[87,98,132],"algebra,":[88,99],"set":[91],"center":[95],"which":[100],"makes":[101],"situations":[103],"just":[104],"like":[105],"case.":[109,117],"this":[111,119],"paper,":[112],"we":[113,134],"study":[114],"non-normal":[116],"case,":[120],"discussion":[122],"becomes":[123],"more":[124],"complicated.":[125],"Using":[126],"representations":[128],"$D_n$,":[133],"show":[135],"${\\rm":[137,155],"Cay}(D_n,S)$":[138,156],"cannot":[139],"PST":[141],"if":[142,154],"$n$":[143],"odd.":[145],"For":[146],"even":[147],"integers":[148],"$n$,":[149],"it":[150],"proved":[152],"PST,":[158],"then":[159],"$S$":[160],"normal.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
