{"id":"https://openalex.org/W1984766600","doi":"https://doi.org/10.1142/s0219265908002163","title":"EXTREMAL CAYLEY GRAPHS OF FINITE CYCLIC GROUPS","display_name":"EXTREMAL CAYLEY GRAPHS OF FINITE CYCLIC GROUPS","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W1984766600","doi":"https://doi.org/10.1142/s0219265908002163","mag":"1984766600"},"language":"en","primary_location":{"id":"doi:10.1142/s0219265908002163","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219265908002163","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/A5100362482","display_name":"Joseph Lee","orcid":"https://orcid.org/0000-0001-7006-5916"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JOSEPH J. LEE","raw_affiliation_strings":["Harvard School of Engineering and Applied Sciences, Harvard University, 29 Oxford St. Cambridge, MA 02138, USA"],"affiliations":[{"raw_affiliation_string":"Harvard School of Engineering and Applied Sciences, Harvard University, 29 Oxford St. Cambridge, MA 02138, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016493666","display_name":"Elysia J. Sheu","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ELYSIA J. SHEU","raw_affiliation_strings":["Sibley School of Mechanical and Aerospace Engineering, Cornell University, 105 Upson Hall, Ithaca, NY 14853, USA","Sibley School of Mechanical and Aerospace Engineering, Cornell University, 105 Upson Hall, Ithaca, NY, 14853, USA"],"affiliations":[{"raw_affiliation_string":"Sibley School of Mechanical and Aerospace Engineering, Cornell University, 105 Upson Hall, Ithaca, NY 14853, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Sibley School of Mechanical and Aerospace Engineering, Cornell University, 105 Upson Hall, Ithaca, NY, 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"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, TX 78666, USA","Department of Mathematics, Texas State University, San Marcos, TX, 78666, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas State University, San Marcos, TX 78666, USA","institution_ids":["https://openalex.org/I13511017"]},{"raw_affiliation_string":"Department of Mathematics, Texas State University, San Marcos, TX, 78666, USA","institution_ids":["https://openalex.org/I13511017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100362482"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":0.4005,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64632863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"09","issue":"01n02","first_page":"73","last_page":"82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"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/T10849","display_name":"Finite Group Theory Research","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.8740478754043579},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8333329558372498},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7546671628952026},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6882333755493164},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.662720799446106},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6363508701324463},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.5544334650039673},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4872402250766754},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.43592262268066406},{"id":"https://openalex.org/keywords/generating-set-of-a-group","display_name":"Generating set of a group","score":0.4165259301662445},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.4159906208515167},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4028680920600891},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.33406946063041687},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08402875065803528}],"concepts":[{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.8740478754043579},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8333329558372498},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7546671628952026},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6882333755493164},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.662720799446106},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6363508701324463},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.5544334650039673},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4872402250766754},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.43592262268066406},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.4165259301662445},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4159906208515167},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4028680920600891},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.33406946063041687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08402875065803528},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":1,"locations":[{"id":"doi:10.1142/s0219265908002163","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219265908002163","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W419638019","https://openalex.org/W623038018","https://openalex.org/W1968194367","https://openalex.org/W1990682154","https://openalex.org/W2063366662","https://openalex.org/W2077736855","https://openalex.org/W2087288544","https://openalex.org/W2092940828","https://openalex.org/W2094613978","https://openalex.org/W2126441872","https://openalex.org/W2133003613"],"related_works":["https://openalex.org/W2364040885","https://openalex.org/W4287865050","https://openalex.org/W3009026414","https://openalex.org/W3107537664","https://openalex.org/W3007853397","https://openalex.org/W2089432291","https://openalex.org/W2048181522","https://openalex.org/W4288119106","https://openalex.org/W2971488975","https://openalex.org/W4221157242"],"abstract_inverted_index":{"Let":[0,61],"\u0393":[1,18,30],"be":[2,45],"a":[3,7,74],"finite":[4],"group":[5,112],"with":[6,27],"nonempty":[8],"subset":[9],"A.":[10,60],"The":[11],"Cayley":[12],"graph":[13,50],"Cay":[14,41,98],"(\u0393,":[15,42],"A)":[16,43],"of":[17,76,95,97,113],"generated":[19],"by":[20],"A":[21,55,78],"is":[22,102,109,119,129],"defined":[23],"as":[24,47],"the":[25,66,89,110],"digraph":[26],"vertex":[28],"set":[29,33,75],"and":[31],"edge":[32],"{(x,y)":[34],"|":[35],"x":[36,52,58],"-1":[37,53],"y":[38],"\u2208":[39,54,59],"A}.":[40],"can":[44],"regarded":[46],"an":[48],"undirected":[49],"if":[51],"for":[56],"all":[57,93],"[Formula:":[62,125,133],"see":[63,126,134],"text]":[64,127,135],"denote":[65],"largest":[67],"integer":[68],"M":[69,100,108],"so":[70],"that":[71,88,124,132],"there":[72],"exists":[73],"integers":[77],"=":[79],"{\u00b11,":[80],"\u00b1a":[81,84],"2":[82],";\u2026,":[83],"k":[85],"}":[86],"such":[87],"average":[90],"distance":[91],"between":[92],"pairs":[94],"vertices":[96],"(\u2124":[99],",A)":[101],"at":[103],"most":[104],"r,":[105],"where":[106],"\u2124":[107],"additive":[111],"residue":[114],"classes":[115],"modulo":[116],"M.":[117],"It":[118,128],"proved":[120,131],"in":[121],"this":[122],"paper":[123],"also":[130]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}