{"id":"https://openalex.org/W4416951838","doi":"https://doi.org/10.1007/s00373-025-03001-9","title":"On the Automorphisms of Token Graphs Generated by 2-cuts with the Same Neighbours","display_name":"On the Automorphisms of Token Graphs Generated by 2-cuts with the Same Neighbours","publication_year":2025,"publication_date":"2025-12-03","ids":{"openalex":"https://openalex.org/W4416951838","doi":"https://doi.org/10.1007/s00373-025-03001-9"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-025-03001-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-03001-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-03001-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-03001-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002294363","display_name":"Ruy Fabila\u2010Monroy","orcid":"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":true,"raw_author_name":"Ruy Fabila-Monroy","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, CINVESTAV, Ciudad de M\u00e9xico, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, CINVESTAV, Ciudad de M\u00e9xico, M\u00e9xico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5094063840","display_name":"Sergio Gerardo G\u00f3mez-Galicia","orcid":null},"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":"Sergio Gerardo G\u00f3mez-Galicia","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, CINVESTAV, Ciudad de M\u00e9xico, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, CINVESTAV, Ciudad de M\u00e9xico, M\u00e9xico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093445825","display_name":"Daniel Gregorio-Longino","orcid":null},"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":"Daniel Gregorio-Longino","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, CINVESTAV, Ciudad de M\u00e9xico, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, CINVESTAV, Ciudad de M\u00e9xico, M\u00e9xico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076667566","display_name":"Teresa I. Hoekstra-Mendoza","orcid":"https://orcid.org/0000-0002-8012-6054"},"institutions":[{"id":"https://openalex.org/I124618812","display_name":"Mathematics Research Center","ror":"https://ror.org/02nhmp827","country_code":"MX","type":"facility","lineage":["https://openalex.org/I124618812"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Teresa I. Hoekstra-Mendoza","raw_affiliation_strings":["Centro de Investigaci\u00f3n en Matem\u00e1ticas, CIMAT, Guanajuato, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Investigaci\u00f3n en Matem\u00e1ticas, CIMAT, Guanajuato, M\u00e9xico","institution_ids":["https://openalex.org/I124618812"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066446790","display_name":"Ana Laura Trujillo-Negrete","orcid":"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":"Ana Trujillo-Negrete","raw_affiliation_strings":["Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico, M\u00e9xico"],"raw_orcid":"https://orcid.org/0000-0002-1138-1190","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico, M\u00e9xico","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5002294363"],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35400622,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"1","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":0.4936999976634979,"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":0.4936999976634979,"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/T10849","display_name":"Finite Group Theory Research","score":0.16670000553131104,"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/T11476","display_name":"Graph theory and applications","score":0.07490000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.8508999943733215},{"id":"https://openalex.org/keywords/graph-automorphism","display_name":"Graph automorphism","score":0.6789000034332275},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.5522000193595886},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5418000221252441},{"id":"https://openalex.org/keywords/vertex-transitive-graph","display_name":"Vertex-transitive graph","score":0.5066999793052673},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.4291999936103821},{"id":"https://openalex.org/keywords/symmetric-graph","display_name":"Symmetric graph","score":0.39169999957084656},{"id":"https://openalex.org/keywords/automorphisms-of-the-symmetric-and-alternating-groups","display_name":"Automorphisms of the symmetric and alternating groups","score":0.32659998536109924}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.8508999943733215},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8467000126838684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8307999968528748},{"id":"https://openalex.org/C6049932","wikidata":"https://www.wikidata.org/wiki/Q834981","display_name":"Graph automorphism","level":5,"score":0.6789000034332275},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.5522000193595886},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5418000221252441},{"id":"https://openalex.org/C113203676","wikidata":"https://www.wikidata.org/wiki/Q220997","display_name":"Vertex-transitive graph","level":5,"score":0.5066999793052673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45719999074935913},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.4291999936103821},{"id":"https://openalex.org/C14201764","wikidata":"https://www.wikidata.org/wiki/Q1205074","display_name":"Symmetric graph","level":5,"score":0.39169999957084656},{"id":"https://openalex.org/C162619202","wikidata":"https://www.wikidata.org/wiki/Q4826703","display_name":"Automorphisms of the symmetric and alternating groups","level":3,"score":0.32659998536109924},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.30219998955726624},{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.28929999470710754},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.2800000011920929},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.27090001106262207},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.27000001072883606},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.2549000084400177},{"id":"https://openalex.org/C150433608","wikidata":"https://www.wikidata.org/wiki/Q5337633","display_name":"Edge-graceful labeling","level":5,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-025-03001-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-03001-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-03001-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00373-025-03001-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-03001-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-03001-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1704385109","display_name":null,"funder_award_id":"FORDECYT-PRONACES/39570/2020","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"},{"id":"https://openalex.org/G6074722199","display_name":"STRUCTURAL GRAPH THEORY FOR TOKEN GRAPHS AND THE TREE CONTAINMENT PROBLEM.","funder_award_id":"3220838","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"},{"id":"https://openalex.org/G6372923606","display_name":null,"funder_award_id":"Postdoctorado 3220838","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"},{"id":"https://openalex.org/G8167787340","display_name":null,"funder_award_id":"FB210005","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"}],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"},{"id":"https://openalex.org/F4320323401","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25"},{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416951838.pdf"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2913469604","https://openalex.org/W2961346124","https://openalex.org/W4230191592","https://openalex.org/W4238591275","https://openalex.org/W4319660215","https://openalex.org/W4414279623"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"G":[2,35,65,80,85,130,196,209],"be":[3],"a":[4,106,126,165],"connected":[5],"graph":[6,33,38],"on":[7],"n":[8],"vertices":[9,56,63],"and":[10,135],"$$1":[11],"\\le":[12,14],"k":[13,31,60],"n-1$$":[15],"<mml:math":[16,40,91,112,144,172],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[17,41,92,113,145,173],"<mml:mrow>":[18,42,47,93,98,114,146,174,179],"<mml:mn>1</mml:mn>":[19,25],"<mml:mo>\u2264</mml:mo>":[20,22],"<mml:mi>k</mml:mi>":[21,45,96,177],"<mml:mi>n</mml:mi>":[23],"<mml:mo>-</mml:mo>":[24],"</mml:mrow>":[26,51,52,102,103,123,154,183,184],"</mml:math>":[27,53,104,124,155,185],"an":[28,77,87],"integer.":[29],"The":[30],"-token":[32],"of":[34,62,64,68,79,84,89,129,168,170,195,208],"is":[36,76,125],"the":[37,59,138,201],"$$F_k(G)$$":[39,90,171],"<mml:msub>":[43,94,175],"<mml:mi>F</mml:mi>":[44,95,176],"</mml:msub>":[46,97,178],"<mml:mo>(</mml:mo>":[48,99,180],"<mml:mi>G</mml:mi>":[49,100,147,181],"<mml:mo>)</mml:mo>":[50,101,182],",":[54,66,131],"whose":[55],"are":[57,70,190],"all":[58,205],"-subsets":[61],"two":[67],"which":[69],"adjacent":[71],"whenever":[72],"their":[73],"symmetric":[74],"difference":[75],"edge":[78],".":[81,156,197,210],"Every":[82],"automorphism":[83,88],"induces":[86],"in":[105,141],"natural":[107],"way.":[108],"Suppose":[109],"that":[110,133,162,189],"$$S:=\\{x,y\\}$$":[111],"<mml:mi>S</mml:mi>":[115],"<mml:mo>:</mml:mo>":[116],"<mml:mo>=</mml:mo>":[117],"<mml:mo>{</mml:mo>":[118,149],"<mml:mi>x</mml:mi>":[119,150],"<mml:mo>,</mml:mo>":[120,151],"<mml:mi>y</mml:mi>":[121,152],"<mml:mo>}</mml:mo>":[122,153],"cut":[127],"set":[128],"such":[132,206],"x":[134],"y":[136],"have":[137],"same":[139],"neighbours":[140],"$$G\\setminus":[142],"\\{x,y\\}$$":[143],"<mml:mo>\\</mml:mo>":[148],"In":[157],"this":[158],"paper,":[159],"we":[160],"show":[161],"there":[163],"exists":[164],"large":[166],"number":[167],"automorphisms":[169,194],"defined":[186],"by":[187,193,204],"S":[188],"not":[191],"induced":[192],"We":[198],"also":[199],"describe":[200],"group":[202],"produced":[203],"2-cuts":[207]},"counts_by_year":[],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-12-03T00:00:00"}