{"id":"https://openalex.org/W2887073945","doi":"https://doi.org/10.1142/s1793830921500221","title":"Counting short cycles of (c,d)-regular bipartite graphs","display_name":"Counting short cycles of (c,d)-regular bipartite graphs","publication_year":2020,"publication_date":"2020-09-16","ids":{"openalex":"https://openalex.org/W2887073945","doi":"https://doi.org/10.1142/s1793830921500221","mag":"2887073945"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830921500221","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921500221","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.00352","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064823802","display_name":"Mohsen Alinejad","orcid":null},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M. Alinejad","raw_affiliation_strings":["Department of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775 Mashhad, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775 Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067556620","display_name":"Kazem Khashyarmanesh","orcid":"https://orcid.org/0000-0003-3314-7298"},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"K. Khashyarmanesh","raw_affiliation_strings":["Department of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775 Mashhad, Iran"],"raw_orcid":"https://orcid.org/0000-0003-3314-7298","affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775 Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064823802"],"corresponding_institution_ids":["https://openalex.org/I86958956"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00736234,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"03","first_page":"2150022","last_page":"2150022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","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/T11321","display_name":"Error Correcting Code Techniques","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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T12029","display_name":"DNA and Biological Computing","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8385961055755615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7968422174453735},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7854560017585754},{"id":"https://openalex.org/keywords/tanner-graph","display_name":"Tanner graph","score":0.7135816812515259},{"id":"https://openalex.org/keywords/foster-graph","display_name":"Foster graph","score":0.6023138165473938},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.5962469577789307},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5275121331214905},{"id":"https://openalex.org/keywords/odd-graph","display_name":"Odd graph","score":0.5271120667457581},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.48318710923194885},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4716559946537018},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.4684310853481293},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.465238481760025},{"id":"https://openalex.org/keywords/regular-graph","display_name":"Regular graph","score":0.4533797800540924},{"id":"https://openalex.org/keywords/triangle-free-graph","display_name":"Triangle-free graph","score":0.4341651499271393},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.35874173045158386},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.3409609794616699},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3128134608268738},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.297485888004303},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.13491955399513245},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11593666672706604}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8385961055755615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7968422174453735},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7854560017585754},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.7135816812515259},{"id":"https://openalex.org/C68996132","wikidata":"https://www.wikidata.org/wiki/Q3115485","display_name":"Foster graph","level":5,"score":0.6023138165473938},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.5962469577789307},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5275121331214905},{"id":"https://openalex.org/C206815938","wikidata":"https://www.wikidata.org/wiki/Q7077445","display_name":"Odd graph","level":5,"score":0.5271120667457581},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.48318710923194885},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4716559946537018},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.4684310853481293},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.465238481760025},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.4533797800540924},{"id":"https://openalex.org/C114727528","wikidata":"https://www.wikidata.org/wiki/Q7840044","display_name":"Triangle-free graph","level":5,"score":0.4341651499271393},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35874173045158386},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3409609794616699},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3128134608268738},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.297485888004303},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.13491955399513245},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11593666672706604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C46462455","wikidata":"https://www.wikidata.org/wiki/Q5395712","display_name":"Error floor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s1793830921500221","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921500221","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1808.00352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.00352","pdf_url":"https://arxiv.org/pdf/1808.00352","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2887073945","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1808.00352","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1808.00352","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1808.00352","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.00352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.00352","pdf_url":"https://arxiv.org/pdf/1808.00352","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2887073945.pdf","grobid_xml":"https://content.openalex.org/works/W2887073945.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W593236292","https://openalex.org/W652942047","https://openalex.org/W1813544306","https://openalex.org/W1964402820","https://openalex.org/W2119604283","https://openalex.org/W2127221638","https://openalex.org/W2127490352","https://openalex.org/W2133068391","https://openalex.org/W2137874581","https://openalex.org/W2154297943","https://openalex.org/W2154993501","https://openalex.org/W2156541068","https://openalex.org/W2574730918","https://openalex.org/W2579410364","https://openalex.org/W2806758424","https://openalex.org/W4252676889"],"related_works":["https://openalex.org/W2981974404","https://openalex.org/W1966042168","https://openalex.org/W1999854368","https://openalex.org/W2040611023","https://openalex.org/W90744597","https://openalex.org/W2476038563","https://openalex.org/W2962683955","https://openalex.org/W2765383521","https://openalex.org/W2139618349","https://openalex.org/W2184278829","https://openalex.org/W3180474026","https://openalex.org/W2033687719","https://openalex.org/W2072838067","https://openalex.org/W2979276937","https://openalex.org/W37585774","https://openalex.org/W3123563708","https://openalex.org/W2147539398","https://openalex.org/W2963883188","https://openalex.org/W2953180795","https://openalex.org/W2963794656"],"abstract_inverted_index":{"Recently,":[0],"Tanner":[1,24],"graphs":[2,25,45,159],"which":[3,190],"represented":[4],"low":[5],"density":[6],"parity":[7],"check":[8],"(LDPC)":[9],"codes":[10],"have":[11],"become":[12],"an":[13],"interesting":[14],"research":[15],"topic.":[16],"Finding":[17],"the":[18,32,40,48,54,63,78,105,113,137,150,153,162,167,173],"number":[19,64,79,138,174],"of":[20,23,34,36,42,53,65,80,82,107,115,139,141,156,169,175,182],"short":[21],"cycles":[22,35,81,114,140],"motivated":[26],"Blake":[27],"and":[28,50,75,87,100,152,172,186],"Lin":[29],"to":[30,39,61,69],"investigate":[31],"multiplicity":[33],"length":[37,83,116,142],"equal":[38],"girth":[41,106],"bi-regular":[43,97,123,157],"bipartite":[44,98,124,158],"by":[46,148],"using":[47,149],"spectrum":[49,151],"degree":[51,154],"distribution":[52,155],"graph.":[55],"While":[56],"there":[57],"were":[58],"many":[59],"algorithms":[60],"find":[62,136],"cycles,":[66],"they":[67,126],"chose":[68],"take":[70],"a":[71,96,129],"computational":[72],"approach.":[73],"Dehghan":[74],"Banihashemi":[76],"counted":[77],"[Formula:":[84,88,92,101,108,119,145,183,187],"see":[85,89,93,102,109,120,146,184,188],"text]":[86,90,94,103,110,121,147,185,189],"where":[91],"is":[95,104],"graph":[99],"But":[111],"for":[112],"smaller":[117],"than":[118,144],"in":[122],"graphs,":[125],"only":[127,165],"proposed":[128],"descriptive":[130],"technique.":[131],"In":[132],"this":[133],"paper,":[134],"we":[135],"less":[143],"such":[160],"that":[161],"formula":[163],"depends":[164],"on":[166],"partitions":[168],"positive":[170],"integers":[171],"closed":[176],"cycle-free":[177],"walks":[178],"from":[179],"any":[180],"vertex":[181],"are":[191],"known.":[192]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}