{"id":"https://openalex.org/W4287959418","doi":"https://doi.org/10.1142/s1793830922501294","title":"Equitable partition for some Ramanujan graphs","display_name":"Equitable partition for some Ramanujan graphs","publication_year":2022,"publication_date":"2022-07-26","ids":{"openalex":"https://openalex.org/W4287959418","doi":"https://doi.org/10.1142/s1793830922501294"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922501294","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501294","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":"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/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, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran"],"raw_orcid":"https://orcid.org/0000-0001-6818-3753","affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015892788","display_name":"Ahmad Erfanian","orcid":"https://orcid.org/0000-0002-9637-1417"},"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":"A. Erfanian","raw_affiliation_strings":["Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, 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/A5033094538","display_name":"S. Fulad","orcid":null},"institutions":[{"id":"https://openalex.org/I166459259","display_name":"Shiraz University","ror":"https://ror.org/028qtbk54","country_code":"IR","type":"education","lineage":["https://openalex.org/I166459259"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"S. Fulad","raw_affiliation_strings":["Department of Mathematics, School of Science, Shiraz University, P.O. Box 7146713565, Shiraz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Shiraz University, P.O. Box 7146713565, Shiraz, Iran","institution_ids":["https://openalex.org/I166459259"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15988474,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"05","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6887718439102173},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.671604335308075},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.637969434261322},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.6207935810089111},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5514289140701294},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5451880693435669},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.545160174369812},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.52232426404953},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45285820960998535},{"id":"https://openalex.org/keywords/graph-product","display_name":"Graph product","score":0.43203204870224},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.373323917388916},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.2809979319572449},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.2410641312599182},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19952163100242615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6887718439102173},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.671604335308075},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.637969434261322},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.6207935810089111},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5514289140701294},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5451880693435669},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.545160174369812},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.52232426404953},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45285820960998535},{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.43203204870224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.373323917388916},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.2809979319572449},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.2410641312599182},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19952163100242615},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922501294","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501294","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1971907125","https://openalex.org/W1991771574","https://openalex.org/W2012273627","https://openalex.org/W2020097440","https://openalex.org/W2036871172","https://openalex.org/W2058056091","https://openalex.org/W2130270608","https://openalex.org/W2132266826","https://openalex.org/W2142408004","https://openalex.org/W2983588208","https://openalex.org/W4235946010","https://openalex.org/W4238591275","https://openalex.org/W4245662714"],"related_works":["https://openalex.org/W2366404817","https://openalex.org/W2963905608","https://openalex.org/W3086542228","https://openalex.org/W2997280357","https://openalex.org/W2775050868","https://openalex.org/W2081426440","https://openalex.org/W2963699585","https://openalex.org/W2287003313","https://openalex.org/W3025390008","https://openalex.org/W4309747353"],"abstract_inverted_index":{"For":[0],"a":[1,16,44,70,100,104],"[Formula:":[2,6,11,30,93,107],"see":[3,7,12,31,94,108],"text]-regular":[4],"graph":[5,41,92],"text],":[8,95],"an":[9],"edge-signing":[10],"text]":[13],"is":[14],"called":[15],"good":[17,45,71,89,101],"signing":[18,72,102],"if":[19,85],"the":[20,52,59],"absolute":[21],"eigenvalues":[22],"of":[23,54,80,106],"its":[24],"adjacency":[25],"matrix":[26],"are":[27],"at":[28],"most":[29],"text].":[32,109],"Bilu":[33],"and":[34,77],"Linial":[35],"conjectured":[36],"that":[37],"for":[38,61,73,91,103],"each":[39],"regular":[40],"there":[42,86],"exists":[43],"signing.":[46],"In":[47,83],"this":[48],"paper,":[49],"by":[50],"using":[51],"concept":[53],"\u201cEquitable":[55],"Partition\u201d,":[56],"we":[57,97],"prove":[58],"conjecture":[60],"some":[62],"cases.":[63],"We":[64],"show":[65],"how":[66],"to":[67],"find":[68,99],"out":[69],"special":[74],"complete":[75],"graphs":[76],"lexicographic":[78],"product":[79],"two":[81,88],"graphs.":[82],"particular,":[84],"exist":[87],"signings":[90],"then":[96],"can":[98],"2-lift":[105]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}