{"id":"https://openalex.org/W2008088669","doi":"https://doi.org/10.1142/s0219265911002873","title":"EXTREMAL CAYLEY DIGRAPHS OF FINITE ABELIAN GROUPS","display_name":"EXTREMAL CAYLEY DIGRAPHS OF FINITE ABELIAN GROUPS","publication_year":2011,"publication_date":"2011-03-01","ids":{"openalex":"https://openalex.org/W2008088669","doi":"https://doi.org/10.1142/s0219265911002873","mag":"2008088669"},"language":"en","primary_location":{"id":"doi:10.1142/s0219265911002873","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219265911002873","pdf_url":null,"source":{"id":"https://openalex.org/S63112013","display_name":"Journal of Interconnection Networks","issn_l":"0219-2659","issn":["0219-2659","1793-6713"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Interconnection Networks","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/A5005383688","display_name":"ABBY GAIL MASK","orcid":null},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ABBY GAIL MASK","raw_affiliation_strings":["Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA","institution_ids":["https://openalex.org/I13511017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048536259","display_name":"Joni J. Schneider","orcid":null},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JONI SCHNEIDER","raw_affiliation_strings":["Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA","institution_ids":["https://openalex.org/I13511017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108284194","display_name":"Xing\u2010De Jia","orcid":null},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"XINGDE JIA","raw_affiliation_strings":["Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas State University, San Marcos, Texas 78666, USA","institution_ids":["https://openalex.org/I13511017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I13511017"],"apc_list":null,"apc_paid":null,"fwci":1.0733,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78004065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"01n02","first_page":"125","last_page":"135"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9965999722480774,"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":0.984000027179718,"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/cayley-graph","display_name":"Cayley graph","score":0.8676313161849976},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.8554062843322754},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.8534212112426758},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7454426884651184},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7203845977783203},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6676946878433228},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.5841599702835083},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5777966976165771},{"id":"https://openalex.org/keywords/generating-set-of-a-group","display_name":"Generating set of a group","score":0.5123432874679565},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.48116788268089294},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4783622622489929},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.4362502694129944},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09915095567703247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08114248514175415},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05637064576148987},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.05510282516479492}],"concepts":[{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.8676313161849976},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8554062843322754},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8534212112426758},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7454426884651184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7203845977783203},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6676946878433228},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.5841599702835083},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5777966976165771},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.5123432874679565},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.48116788268089294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4783622622489929},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.4362502694129944},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09915095567703247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08114248514175415},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05637064576148987},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.05510282516479492},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219265911002873","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219265911002873","pdf_url":null,"source":{"id":"https://openalex.org/S63112013","display_name":"Journal of Interconnection Networks","issn_l":"0219-2659","issn":["0219-2659","1793-6713"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Interconnection Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1968194367","https://openalex.org/W1972875764","https://openalex.org/W1990682154","https://openalex.org/W2077736855","https://openalex.org/W2078402463","https://openalex.org/W2094613978","https://openalex.org/W2152267550","https://openalex.org/W2479604145"],"related_works":["https://openalex.org/W2364040885","https://openalex.org/W3009026414","https://openalex.org/W2089432291","https://openalex.org/W3007853397","https://openalex.org/W3107537664","https://openalex.org/W4287865050","https://openalex.org/W2048181522","https://openalex.org/W2971488975","https://openalex.org/W2042747061","https://openalex.org/W4221157242"],"abstract_inverted_index":{"Cayley":[0,18,82,149],"digraphs":[1,19],"of":[2,14,60,80,87,110],"finite":[3,51,145],"abelian":[4,52,146],"groups":[5],"are":[6],"often":[7],"used":[8],"to":[9,155],"model":[10],"communication":[11],"networks.":[12],"Because":[13],"their":[15],"applications,":[16],"extremal":[17],"have":[20],"been":[21],"studied":[22],"extensively":[23],"in":[24],"recent":[25],"years.":[26],"Given":[27],"any":[28],"positive":[29,42,99],"integers":[30,111],"d":[31,134],"and":[32,55,137,158],"k.":[33],"Let":[34],"m":[35,44,101,115],"*":[36],"(d,":[37],"k)":[38,95],"denote":[39,96],"the":[40,78,81,97,144],"largest":[41,98],"integer":[43,100],"such":[45,62,102],"that":[46,63,103,128,143],"there":[47,104],"exists":[48,105],"an":[49],"m-element":[50],"group":[53,147],"\u0393":[54,61,88],"a":[56,106,162],"k-element":[57,107],"subset":[58],"A":[59,109],"diam":[64,72,113],"(":[65,73],"Cay":[66,74,84],"(\u0393,":[67,75,85],"A))":[68,76,117],"\u2264":[69,118],"d,":[70],"where":[71],"denotes":[77],"diameter":[79,157],"digraph":[83,150],"A)":[86],"generated":[89],"by":[90],"A.":[91],"Similarly,":[92],"let":[93],"m(d,":[94],"set":[108],"with":[112,153],"(\u2124":[114],",":[116],"d.":[119],"In":[120],"this":[121],"paper,":[122],"we":[123],"prove,":[124],"among":[125],"other":[126],"results,":[127],"[Formula:":[129],"see":[130],"text]":[131],"for":[132],"all":[133],"\u2265":[135,139],"1":[136],"k":[138],"1.":[140],"This":[141],"means":[142],"whose":[148],"is":[151],"optimal":[152],"respect":[154],"its":[156],"degree":[159],"can":[160],"be":[161],"cyclic":[163],"group.":[164]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
