{"id":"https://openalex.org/W2619873916","doi":"https://doi.org/10.1142/s0218196717500412","title":"The maximal subgroups and the complexity of the flow semigroup of finite (di)graphs","display_name":"The maximal subgroups and the complexity of the flow semigroup of finite (di)graphs","publication_year":2017,"publication_date":"2017-09-04","ids":{"openalex":"https://openalex.org/W2619873916","doi":"https://doi.org/10.1142/s0218196717500412","mag":"2619873916"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196717500412","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196717500412","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"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":"International Journal of Algebra and Computation","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/1705.09577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048167453","display_name":"G\u00e1bor Horv\u00e1th","orcid":"https://orcid.org/0000-0001-9657-1219"},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"G\u00e1bor Horv\u00e1th","raw_affiliation_strings":["Institute of Mathematics, University of Debrecen, Pf. 400, Debrecen, 4002, Hungary"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Debrecen, Pf. 400, Debrecen, 4002, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048759955","display_name":"Chrystopher L. Nehaniv","orcid":"https://orcid.org/0000-0002-7807-1875"},"institutions":[{"id":"https://openalex.org/I141584323","display_name":"University of Hertfordshire","ror":"https://ror.org/0267vjk41","country_code":"GB","type":"education","lineage":["https://openalex.org/I141584323"]},{"id":"https://openalex.org/I1289762815","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I1289762815"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Chrystopher L. Nehaniv","raw_affiliation_strings":["Royal Society Wolfson Biocomputation Research Laboratory, Centre for Computer Science and Informatics Research, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB, UK"],"affiliations":[{"raw_affiliation_string":"Royal Society Wolfson Biocomputation Research Laboratory, Centre for Computer Science and Informatics Research, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB, UK","institution_ids":["https://openalex.org/I141584323","https://openalex.org/I1289762815"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037051710","display_name":"K\u00e1roly Podoski","orcid":null},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"K\u00e1roly Podoski","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, 13\u201315 Re\u00e1ltanoda utca, Budapest, 1053, Hungary"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, 13\u201315 Re\u00e1ltanoda utca, Budapest, 1053, Hungary","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048167453"],"corresponding_institution_ids":["https://openalex.org/I132735039"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08753657,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"07","first_page":"863","last_page":"886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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/T11567","display_name":"semigroups and automata theory","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/T10304","display_name":"Geometric and Algebraic Topology","score":0.984499990940094,"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9746000170707703,"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/semigroup","display_name":"Semigroup","score":0.8279287219047546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8152058124542236},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7125247120857239},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6694823503494263},{"id":"https://openalex.org/keywords/finite-graph","display_name":"Finite graph","score":0.5692627429962158},{"id":"https://openalex.org/keywords/antisymmetric-relation","display_name":"Antisymmetric relation","score":0.5558456182479858},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5482143759727478},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5158849954605103},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4994375705718994},{"id":"https://openalex.org/keywords/strongly-connected-component","display_name":"Strongly connected component","score":0.4486784338951111},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41763120889663696},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.416595458984375}],"concepts":[{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.8279287219047546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8152058124542236},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7125247120857239},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6694823503494263},{"id":"https://openalex.org/C2994516854","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Finite graph","level":3,"score":0.5692627429962158},{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.5558456182479858},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5482143759727478},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5158849954605103},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4994375705718994},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.4486784338951111},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41763120889663696},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.416595458984375},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1142/s0218196717500412","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196717500412","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"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":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:real.mtak.hu:74252","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1705.09577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.09577","pdf_url":"https://arxiv.org/pdf/1705.09577","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":null,"raw_type":null},{"id":"pmh:oai:uhra.herts.ac.uk:2299/19641","is_oa":true,"landing_page_url":"http://hdl.handle.net/2299/19641","pdf_url":"https://arxiv.org/abs/1705.09577","source":{"id":"https://openalex.org/S4306400241","display_name":"University of Hertfordshire Research Archive (University of Hertfordshire)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I141584323","host_organization_name":"University of Hertfordshire","host_organization_lineage":["https://openalex.org/I141584323"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"mag:2619873916","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1705.09577.pdf","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.1705.09577","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1705.09577","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:1705.09577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.09577","pdf_url":"https://arxiv.org/pdf/1705.09577","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":null,"raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G16918428","display_name":null,"funder_award_id":"318202","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G1748000517","display_name":null,"funder_award_id":"NKFIH","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"},{"id":"https://openalex.org/G2630444709","display_name":"Limits of discrete structures","funder_award_id":"617747","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2995423790","display_name":null,"funder_award_id":"ERC_HU","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G3373887191","display_name":null,"funder_award_id":"K109185","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G351308824","display_name":null,"funder_award_id":"K109185","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G3707183902","display_name":null,"funder_award_id":"NKFIH","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G3829048491","display_name":null,"funder_award_id":"FP7/2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3981126665","display_name":null,"funder_award_id":"Seventh Framework Programme","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5593277320","display_name":null,"funder_award_id":"2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5702163051","display_name":null,"funder_award_id":"FP7/2007","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6904936573","display_name":null,"funder_award_id":"ERC_HU_15 118286","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G7675388388","display_name":null,"funder_award_id":"318202","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"},{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null},{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1410927143","https://openalex.org/W1516513172","https://openalex.org/W1585649433","https://openalex.org/W2002055996","https://openalex.org/W2013611695","https://openalex.org/W2048036606","https://openalex.org/W2118966355","https://openalex.org/W2335132016","https://openalex.org/W2505692471","https://openalex.org/W2604247292","https://openalex.org/W3022690009","https://openalex.org/W3216142546","https://openalex.org/W4205325251","https://openalex.org/W4213311856","https://openalex.org/W4234295943"],"related_works":["https://openalex.org/W2135077518","https://openalex.org/W2951765233","https://openalex.org/W2916612041","https://openalex.org/W2046748035","https://openalex.org/W3098240331","https://openalex.org/W2885384653","https://openalex.org/W2066808294","https://openalex.org/W1777634055","https://openalex.org/W2036534180","https://openalex.org/W3001664564","https://openalex.org/W3210209147","https://openalex.org/W2403231810","https://openalex.org/W3194471634","https://openalex.org/W2094832778","https://openalex.org/W1996462091","https://openalex.org/W2268629067","https://openalex.org/W2054119455","https://openalex.org/W81150580","https://openalex.org/W2174782663","https://openalex.org/W2019537926"],"abstract_inverted_index":{"The":[0],"flow":[1,38,65,117],"semigroup,":[2],"introduced":[3],"by":[4],"Rhodes,":[5],"is":[6,94,132],"an":[7],"invariant":[8,14],"for":[9,15,40,75,81,105,140],"digraphs":[10,78],"and":[11,25,52,57,79],"a":[12,120],"complete":[13],"graphs.":[16],"After":[17],"collecting":[18],"previous":[19],"partial":[20],"results":[21],"together,":[22],"we":[23,50,110],"refine":[24],"prove":[26,111],"Rhodes\u2019s":[27,138],"conjecture":[28,139],"on":[29,47,68],"the":[30,33,37,55,60,64,90,113,116],"structure":[31,56],"of":[32,59,63,92,115,119],"maximal":[34,61],"groups":[35],"in":[36],"semigroup":[39,66,118],"finite,":[41],"antisymmetric,":[42],"strongly":[43,124],"connected":[44,122,125],"digraphs.":[45],"Building":[46],"this":[48],"result,":[49],"investigate":[51],"fully":[53],"describe":[54],"actions":[58],"subgroups":[62],"acting":[67],"all":[69,76,82],"but":[70],"[Formula:":[71,83,101,128,133],"see":[72,84,102,129,134],"text]":[73,103,130],"points":[74],"finite":[77,107],"graphs":[80],"text].":[85],"A":[86],"linear":[87],"algorithm":[88],"(in":[89],"number":[91],"edges)":[93],"presented":[95],"to":[96],"determine":[97],"these":[98],"so-called":[99],"\u201cdefect":[100],"groups\u201d":[104],"any":[106],"(di)graph.":[108],"Finally,":[109],"that":[112],"complexity":[114],"2-vertex":[121],"(and":[123],"di)graph":[126],"with":[127],"vertices":[131],"text],":[135],"completely":[136],"confirming":[137],"such":[141],"(di)graphs.":[142]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
