{"id":"https://openalex.org/W1990682154","doi":"https://doi.org/10.1002/net.3230230407","title":"Undirected loop networks","display_name":"Undirected loop networks","publication_year":1993,"publication_date":"1993-07-01","ids":{"openalex":"https://openalex.org/W1990682154","doi":"https://doi.org/10.1002/net.3230230407","mag":"1990682154"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230230407","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230230407","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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/A5100320969","display_name":"Sheng Chen","orcid":"https://orcid.org/0000-0001-6882-600X"},"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":true,"raw_author_name":"Sheng Chen","raw_affiliation_strings":["Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666","Department of Mathematics, Southwest Texas State University, San Marcos, Texas, 78666"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666","institution_ids":["https://openalex.org/I13511017"]},{"raw_affiliation_string":"Department of Mathematics, Southwest Texas State University, San Marcos, Texas, 78666","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":"Xing\u2010De Jia","raw_affiliation_strings":["Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666","Department of Mathematics, Southwest Texas State University, San Marcos, Texas, 78666"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666","institution_ids":["https://openalex.org/I13511017"]},{"raw_affiliation_string":"Department of Mathematics, Southwest Texas State University, San Marcos, Texas, 78666","institution_ids":["https://openalex.org/I13511017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100320969"],"corresponding_institution_ids":["https://openalex.org/I13511017"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.17531908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"4","first_page":"257","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"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":0.9997000098228455,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9829999804496765,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9797999858856201,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7808730602264404},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.7480538487434387},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.697009265422821},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.6814868450164795},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6682447791099548},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5985473394393921},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45954790711402893},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45841002464294434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40612733364105225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15210121870040894},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.055734485387802124}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7808730602264404},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.7480538487434387},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.697009265422821},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.6814868450164795},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6682447791099548},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5985473394393921},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45954790711402893},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45841002464294434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40612733364105225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15210121870040894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.055734485387802124},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230230407","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230230407","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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":7,"referenced_works":["https://openalex.org/W623038018","https://openalex.org/W2013071574","https://openalex.org/W2051905148","https://openalex.org/W2062954789","https://openalex.org/W2086405971","https://openalex.org/W2094613978","https://openalex.org/W6674317083"],"related_works":["https://openalex.org/W2066808294","https://openalex.org/W4226275486","https://openalex.org/W2320114089","https://openalex.org/W2021255209","https://openalex.org/W1968298352","https://openalex.org/W24774503","https://openalex.org/W4386021657","https://openalex.org/W2094835765","https://openalex.org/W3217035751","https://openalex.org/W1994341438"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"M,":[2],"d":[3,19,55,80,93],",":[4,94],"and":[5,20,46,81],"k":[6,21,36,82,100],"be":[7],"positive":[8],"integers.":[9],"We":[10],"say":[11],"that":[12,39],"M":[13,76,91],"is":[14,61,96,109],"feasible":[15,74],"with":[16,44,77],"respect":[17,78],"to":[18,54,79],"if":[22],"there":[23],"exists":[24],"a":[25,58,62,103],"set":[26],"A":[27,47],"=":[28],"{0,":[29],"\u00b1":[30],"1,":[31],"\u00b1a":[32,35],"2":[33],"\u2026,":[34],"}":[37],"such":[38],"the":[40,72,85],"Cayley":[41,59],"graph":[42,60],"associated":[43],"Z/(M)":[45],"has":[48],"diameter":[49],"less":[50],"than":[51],"or":[52],"equal":[53],".":[56,83],"Such":[57],"model":[63],"for":[64,90,106],"undirected":[65],"loop":[66],"communication":[67],"networks.":[68],"Denote":[69],"M(d,":[70,107],"k)":[71,108],"maximal":[73],"number":[75],"In":[84],"paper,":[86],"an":[87],"explicit":[88],"formula":[89],"(":[92],"2)":[95],"obtained.":[97],"Also,":[98],"when":[99],"\u2267":[101],"3,":[102],"lower":[104],"bound":[105],"established.":[110],"\u00a9":[111],"1993":[112],"by":[113],"John":[114],"Wiley":[115],"&":[116],"Sons,":[117],"Inc.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}