{"id":"https://openalex.org/W7214101640","doi":"https://doi.org/10.48550/arxiv.2609.25529","title":"Automorphisms of Token Graphs That Send $4$-Cycles Generated by Two Edges to Cycles Generated by a $4$-Cycle and Two Tokens","display_name":"Automorphisms of Token Graphs That Send $4$-Cycles Generated by Two Edges to Cycles Generated by a $4$-Cycle and Two Tokens","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214101640","doi":"https://doi.org/10.48550/arxiv.2609.25529"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25529","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25529","pdf_url":"https://arxiv.org/pdf/2609.25529","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25529","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002294363","display_name":"Ruy Fabila\u2010Monroy","orcid":"https://orcid.org/0000-0002-2517-0298","observed_orcids":["https://orcid.org/0000-0002-2517-0298"]},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Fabila-Monroy, Ruy","raw_affiliation_strings":["Departamento de Matem\u00e1ticas , CINVESTAV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas , CINVESTAV","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5094063840","display_name":"Sergio Gerardo G\u00f3mez-Galicia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"G\u00f3mez-Galicia, Sergio Gerardo","raw_affiliation_strings":["Departamento de Matem\u00e1ticas , CINVESTAV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas , CINVESTAV","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066446790","display_name":"Ana Laura Trujillo-Negrete","orcid":"https://orcid.org/0000-0002-1138-1190","observed_orcids":["https://orcid.org/0000-0002-1138-1190"]},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Trujillo-Negrete, Ana Laura","raw_affiliation_strings":["Instituto de Matem\u00e1ticas , UNAM , Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1ticas , UNAM , Mexico","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9707000255584717,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9707000255584717,"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/T11476","display_name":"Graph theory and applications","score":0.008700000122189522,"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/T10849","display_name":"Finite Group Theory Research","score":0.006500000134110451,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/token-graphs","display_name":"token graphs","score":0.9660000205039978},{"id":"https://openalex.org/keywords/graph-automorphisms","display_name":"graph automorphisms","score":0.8799999952316284},{"id":"https://openalex.org/keywords/4-cycles","display_name":"4-cycles","score":0.8420000076293945},{"id":"https://openalex.org/keywords/graph-isomorphism","display_name":"graph isomorphism","score":0.7369999885559082},{"id":"https://openalex.org/keywords/complementation","display_name":"complementation","score":0.4309999942779541},{"id":"https://openalex.org/keywords/twin-vertices","display_name":"twin vertices","score":0.38100001215934753}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.7803999781608582},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7773000001907349},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6804999709129333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6741999983787537},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6207000017166138},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.6194999814033508},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43140000104904175},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4009000062942505},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.3127000033855438},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C6049932","wikidata":"https://www.wikidata.org/wiki/Q834981","display_name":"Graph automorphism","level":5,"score":0.2976999878883362},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2612000107765198}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25529","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25529","pdf_url":"https://arxiv.org/pdf/2609.25529","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"text"},{"id":"doi:10.48550/arxiv.2609.25529","doi":"https://doi.org/10.48550/arxiv.2609.25529","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25529","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25529","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25529","pdf_url":"https://arxiv.org/pdf/2609.25529","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214101640.pdf","grobid_xml":"https://content.openalex.org/works/W7214101640.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1506754921","https://openalex.org/W2961346124","https://openalex.org/W4288055057"],"related_works":["https://openalex.org/W4416951838","https://openalex.org/W4414279623","https://openalex.org/W4288055057","https://openalex.org/W2961346124","https://openalex.org/W4416696357","https://openalex.org/W7135236511","https://openalex.org/W7098299957","https://openalex.org/W7221775025","https://openalex.org/W7219689237","https://openalex.org/W4411262581"],"abstract_inverted_index":{"Let":[0],"$G$":[1,10,45,211],"be":[2,228],"a":[3,106,168,175,179,208],"connected":[4],"graph.":[5],"The":[6],"$k$-token":[7],"graph":[8,13],"of":[9,19,22,25,29,40,44,48,56,109,114,126,143],"is":[11,37],"the":[12,92,129,135,140],"$F_k(G)$":[14],"whose":[15,88],"vertex":[16,125,142],"set":[17],"consists":[18],"all":[20],"subsets":[21],"$k$":[23],"vertices":[24,90],"$G$,":[26],"where":[27],"two":[28,89,154,157,165,194,197,205],"them":[30],"are":[31,59,84],"adjacent":[32],"whenever":[33],"their":[34],"symmetric":[35],"difference":[36],"an":[38,148,183],"edge":[39],"$G$.":[41,99],"Every":[42],"automorphism":[43],"induces":[46],"one":[47,121,124,161,201],"$F_k(G)$,":[49],"as":[50],"does":[51],"complementation":[52],"when":[53],"$k=|G|/2$;":[54],"automorphisms":[55,102,146],"this":[57],"form":[58],"called":[60],"\\emph{induced}.":[61],"Fabila-Monroy":[62],"et":[63],"al.\\":[64],"(Graphs":[65],"and":[66,119,212,218],"Combinatorics":[67],"42,":[68],"2026)":[69],"show":[70,223],"that":[71,224],"token":[72,122,136],"graphs":[73],"can":[74,227],"have":[75,91,214],"many":[76],"non-induced":[77,101],"automorphisms,":[78],"arising":[79],"from":[80],"\\emph{twin":[81],"cuts}.":[82],"These":[83,100,145],"cut":[85],"sets":[86],"$\\{x,y\\}$":[87,138,217],"same":[93],"neighbours":[94],"(other":[95],"than":[96],"themselves)":[97],"in":[98],"send":[103,147],"configurations":[104],"with":[105,233],"prescribed":[107],"number":[108],"tokens":[110,155,166,195,206],"on":[111,123,156,167,196,207],"each":[112],"component":[113],"$G\\setminus":[115],"\\{x,y\\}$,":[116],"totalling":[117],"$k-1$,":[118],"exactly":[120],"$\\{x,y\\}$,":[127],"to":[128,139,160,200],"configuration":[130],"obtained":[131],"by":[132,152,163,192,203,230],"moving":[133,153,164,193,204],"(\\emph{flipping})":[134],"at":[137],"other":[141],"$\\{x,y\\}$.":[144],"induced":[149],"$4$-cycle":[150,190],"generated":[151,162,191,202],"disjoint":[158,198],"edges":[159,199],"$4$-cycle;":[169],"thus":[170],"introducing":[171],"what":[172],"we":[173],"call":[174],"\\emph{twist}.":[176],"We":[177,221],"prove":[178],"partial":[180],"converse:":[181],"if":[182],"isomorphism":[184],"$\u03c6\\colon":[185],"F_k(G)\\to":[186],"F_{k'}(G')$":[187],"sends":[188],"some":[189],"$4$-cycle,":[209],"then":[210],"$G'$":[213],"twin":[215],"cuts":[216],"$\\{x',y'\\}$,":[219],"respectively.":[220],"also":[222],"any":[225],"twist":[226],"undone":[229],"composing":[231],"$\u03c6$":[232],"twin-cut":[234],"flips.":[235]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}