{"id":"https://openalex.org/W2149335813","doi":"https://doi.org/10.1137/0406050","title":"Representations of Borel Cayley Graphs","display_name":"Representations of Borel Cayley Graphs","publication_year":1993,"publication_date":"1993-11-01","ids":{"openalex":"https://openalex.org/W2149335813","doi":"https://doi.org/10.1137/0406050","mag":"2149335813"},"language":"en","primary_location":{"id":"doi:10.1137/0406050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0406050","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5108506740","display_name":"K. Wendy Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"K. Wendy Tang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041940608","display_name":"Bruce W. Arden","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruce W. Arden","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108506740"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4611,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.7253858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":"4","first_page":"655","last_page":"676"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9900000095367432,"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":0.9696000218391418,"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/mathematics","display_name":"Mathematics","score":0.8325958251953125},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.8252350091934204},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.8055852651596069},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7341144680976868},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.6253156661987305},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.5917103290557861},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5273013114929199},{"id":"https://openalex.org/keywords/modular-decomposition","display_name":"Modular decomposition","score":0.5218945145606995},{"id":"https://openalex.org/keywords/vertex-transitive-graph","display_name":"Vertex-transitive graph","score":0.4688623547554016},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.41793370246887207},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.31024932861328125},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.29763081669807434},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.14735737442970276}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8325958251953125},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.8252350091934204},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.8055852651596069},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7341144680976868},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.6253156661987305},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.5917103290557861},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5273013114929199},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.5218945145606995},{"id":"https://openalex.org/C113203676","wikidata":"https://www.wikidata.org/wiki/Q220997","display_name":"Vertex-transitive graph","level":5,"score":0.4688623547554016},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.41793370246887207},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.31024932861328125},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.29763081669807434},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.14735737442970276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0406050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0406050","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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":16,"referenced_works":["https://openalex.org/W606008011","https://openalex.org/W1964735684","https://openalex.org/W1973924721","https://openalex.org/W1974558557","https://openalex.org/W1983371431","https://openalex.org/W2002281184","https://openalex.org/W2013259664","https://openalex.org/W2015235100","https://openalex.org/W2044467672","https://openalex.org/W2073491596","https://openalex.org/W2077534920","https://openalex.org/W2085319748","https://openalex.org/W2104852618","https://openalex.org/W2119733312","https://openalex.org/W2150512804","https://openalex.org/W4255308777"],"related_works":["https://openalex.org/W4287117052","https://openalex.org/W2149335813","https://openalex.org/W1469467629","https://openalex.org/W2965619662","https://openalex.org/W1510673395","https://openalex.org/W2526622610","https://openalex.org/W2963129861","https://openalex.org/W1991382630","https://openalex.org/W2044603295","https://openalex.org/W4302971558"],"abstract_inverted_index":{"There":[0],"is":[1,95,132],"a":[2,26,52,115,129],"continuing":[3],"search":[4],"for":[5,51],"dense":[6],"$(":[7,45],"\\delta":[8,46],",D":[9],")$":[10,49],"interconnection":[11],"graphs,":[12],"that":[13,80,97],"is,":[14],"regular,":[15],"undirected,":[16],"degree":[17],"$\\delta":[18],"$":[19],"graphs":[20,32,50,64,83,102],"with":[21],"diameter":[22],"D":[23,55],"and":[24],"having":[25],"large":[27],"number":[28],"of":[29,41,54,62,68],"nodes.":[30],"Cayley":[31,82,101,126],"formed":[33],"by":[34,107],"Borel":[35,100,125],"subgroups":[36],"currently":[37],"contribute":[38],"to":[39,121,137],"some":[40],"the":[42,58,66,108],"densest":[43],"known":[44],"=":[47],"4,D":[48],"range":[53],"[1].":[56],"However,":[57],"group":[59],"theoretic":[60],"representation":[61],"these":[63],"makes":[65],"development":[67],"efficient":[69],"routing":[70],"algorithms":[71],"difficult.":[72],"In":[73,91],"an":[74],"earlier":[75],"report,":[76],"it":[77,94],"was":[78],"shown":[79,96],"all":[81,98],"have":[84],"generalized":[85],"chordal":[86,111],"ring":[87],"(GCR)":[88],"representations":[89],"[2].":[90],"this":[92,139],"paper,":[93],"degree-4":[99,124],"can":[103],"also":[104],"be":[105],"represented":[106],"more":[109],"restrictive":[110],"rings":[112],"(CR)":[113],"through":[114],"constructive":[116],"proof.":[117],"A":[118],"step-by-step":[119],"algorithm":[120],"transform":[122],"any":[123],"graph":[127,131],"into":[128],"CR":[130],"provided.":[133],"Examples":[134],"are":[135],"used":[136],"illustrate":[138],"concept.":[140]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
