{"id":"https://openalex.org/W1828162091","doi":"https://doi.org/10.37236/671","title":"Some Results for the Periodicity and Perfect State Transfer","display_name":"Some Results for the Periodicity and Perfect State Transfer","publication_year":2011,"publication_date":"2011-09-20","ids":{"openalex":"https://openalex.org/W1828162091","doi":"https://doi.org/10.37236/671","mag":"1828162091"},"language":"en","primary_location":{"id":"doi:10.37236/671","is_oa":true,"landing_page_url":"https://doi.org/10.37236/671","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p184/pdf","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":null,"license_id":null,"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://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p184/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019475169","display_name":"Jiang Zhou","orcid":"https://orcid.org/0000-0003-1541-5316"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiang Zhou","raw_affiliation_strings":["College of Science Harbin Engineering University Harbin 150001, P.R. China"],"affiliations":[{"raw_affiliation_string":"College of Science Harbin Engineering University Harbin 150001, P.R. China","institution_ids":["https://openalex.org/I151727225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063685290","display_name":"Changjiang Bu","orcid":"https://orcid.org/0000-0002-9564-5447"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changjiang Bu","raw_affiliation_strings":["College of Science Harbin Engineering University Harbin 150001, P.R. China","Harbin Engineering University"],"affiliations":[{"raw_affiliation_string":"College of Science Harbin Engineering University Harbin 150001, P.R. China","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"Harbin Engineering University","institution_ids":["https://openalex.org/I151727225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040210816","display_name":"Jihong Shen","orcid":"https://orcid.org/0000-0002-2333-3428"},"institutions":[{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jihong Shen","raw_affiliation_strings":["College of Science Harbin Engineering University Harbin 150001, P.R. China","Harbin Engineering University"],"affiliations":[{"raw_affiliation_string":"College of Science Harbin Engineering University Harbin 150001, P.R. China","institution_ids":["https://openalex.org/I151727225"]},{"raw_affiliation_string":"Harbin Engineering University","institution_ids":["https://openalex.org/I151727225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019475169"],"corresponding_institution_ids":["https://openalex.org/I151727225"],"apc_list":null,"apc_paid":null,"fwci":0.7395,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.65790097,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9975000023841858,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9970999956130981,"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/antipodal-point","display_name":"Antipodal point","score":0.8948789238929749},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8498970866203308},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8112473487854004},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6850060820579529},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6077472567558289},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5978557467460632},{"id":"https://openalex.org/keywords/transfer","display_name":"Transfer (computing)","score":0.5710054039955139},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.501004695892334},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.48555800318717957},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.47170472145080566},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42393144965171814},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06392177939414978},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06237491965293884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05950912833213806}],"concepts":[{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.8948789238929749},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8498970866203308},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8112473487854004},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6850060820579529},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6077472567558289},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5978557467460632},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.5710054039955139},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.501004695892334},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.48555800318717957},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.47170472145080566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42393144965171814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06392177939414978},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06237491965293884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05950912833213806},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/671","is_oa":true,"landing_page_url":"https://doi.org/10.37236/671","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p184/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.5794","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.5794","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v18i1p184/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/671","is_oa":true,"landing_page_url":"https://doi.org/10.37236/671","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p184/pdf","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":null,"license_id":null,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1828162091.pdf","grobid_xml":"https://content.openalex.org/works/W1828162091.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W57448092","https://openalex.org/W593236292","https://openalex.org/W1546248008","https://openalex.org/W1988243055","https://openalex.org/W2030613261","https://openalex.org/W2060823538","https://openalex.org/W2065493715","https://openalex.org/W2076585714","https://openalex.org/W2077488909","https://openalex.org/W2084311741","https://openalex.org/W2121700246","https://openalex.org/W2131552237","https://openalex.org/W2138033161","https://openalex.org/W2612937485","https://openalex.org/W3123104679","https://openalex.org/W4237658155","https://openalex.org/W4296411925","https://openalex.org/W4298236575"],"related_works":["https://openalex.org/W16605181","https://openalex.org/W3088694259","https://openalex.org/W2485184685","https://openalex.org/W2013157969","https://openalex.org/W4205709123","https://openalex.org/W1828162091","https://openalex.org/W2802868204","https://openalex.org/W2963891256","https://openalex.org/W2950502167","https://openalex.org/W2963726605"],"abstract_inverted_index":{"Let":[0],"$G$":[1,11,63],"be":[2],"a":[3,14,20,51],"graph":[4,16],"with":[5,82],"adjacency":[6],"matrix":[7],"$A$,":[8],"let":[9],"$H(t)=\\exp(itA)$.":[10],"is":[12,26,64,66],"called":[13],"periodic":[15,65],"if":[17,48],"there":[18,49],"exists":[19,50],"time":[21,52],"$\\tau$":[22,53],"such":[23,54],"that":[24,39,55],"$H(\\tau)$":[25],"diagonal.":[27],"If":[28],"$u$":[29,45],"and":[30,59],"$v$":[31,47],"are":[32],"distinct":[33],"vertices":[34,79],"in":[35,80],"$G$,":[36],"we":[37],"say":[38],"perfect":[40,74],"state":[41,75],"transfer":[42,76],"occurs":[43],"from":[44],"to":[46],"$|H(\\tau)_{u,v}|=1$.":[56],"A":[57],"necessary":[58],"sufficient":[60],"condition":[61],"for":[62,72],"given.":[67],"We":[68],"give":[69],"the":[70,73],"existence":[71],"between":[77],"antipodal":[78],"graphs":[81],"extreme":[83],"diameter.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
