{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T07:05:12Z","timestamp":1770966312758,"version":"3.50.1"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T00:00:00Z","timestamp":1764720000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T00:00:00Z","timestamp":1764720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["FORDECYT-PRONACES\/39570\/2020"],"award-info":[{"award-number":["FORDECYT-PRONACES\/39570\/2020"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["FORDECYT-PRONACES\/39570\/2020"],"award-info":[{"award-number":["FORDECYT-PRONACES\/39570\/2020"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["FORDECYT-PRONACES\/39570\/2020"],"award-info":[{"award-number":["FORDECYT-PRONACES\/39570\/2020"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["FORDECYT-PRONACES\/39570\/2020"],"award-info":[{"award-number":["FORDECYT-PRONACES\/39570\/2020"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100020884","name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","doi-asserted-by":"publisher","award":["Postdoctorado 3220838"],"award-info":[{"award-number":["Postdoctorado 3220838"]}],"id":[{"id":"10.13039\/501100020884","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100020884","name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","doi-asserted-by":"publisher","award":["Basal Grant CMM FB210005"],"award-info":[{"award-number":["Basal Grant CMM FB210005"]}],"id":[{"id":"10.13039\/501100020884","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005739","name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","doi-asserted-by":"publisher","award":["UNAM POSDOC"],"award-info":[{"award-number":["UNAM POSDOC"]}],"id":[{"id":"10.13039\/501100005739","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Let\n                    <jats:italic>G<\/jats:italic>\n                    be a connected graph on\n                    <jats:italic>n<\/jats:italic>\n                    vertices and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$1 \\le k \\le n-1$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>\u2264<\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>\u2264<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>-<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    an integer. The\n                    <jats:italic>k<\/jats:italic>\n                    -token graph of\n                    <jats:italic>G<\/jats:italic>\n                    is the graph\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$F_k(G)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>F<\/mml:mi>\n                              <mml:mi>k<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>G<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , whose vertices are all the\n                    <jats:italic>k<\/jats:italic>\n                    -subsets of vertices of\n                    <jats:italic>G<\/jats:italic>\n                    , two of which are adjacent whenever their symmetric difference is an edge of\n                    <jats:italic>G<\/jats:italic>\n                    . Every automorphism of\n                    <jats:italic>G<\/jats:italic>\n                    induces an automorphism of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$F_k(G)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>F<\/mml:mi>\n                              <mml:mi>k<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>G<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    in a natural way. Suppose that\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$S:=\\{x,y\\}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mo>:<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mo>{<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>y<\/mml:mi>\n                            <mml:mo>}<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is a cut set of\n                    <jats:italic>G<\/jats:italic>\n                    , such that\n                    <jats:italic>x<\/jats:italic>\n                    and\n                    <jats:italic>y<\/jats:italic>\n                    have the same neighbours in\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$G\\setminus \\{x,y\\}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>G<\/mml:mi>\n                            <mml:mo>\\<\/mml:mo>\n                            <mml:mo>{<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>y<\/mml:mi>\n                            <mml:mo>}<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . In this paper, we show that there exists a large number of automorphisms of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$F_k(G)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>F<\/mml:mi>\n                              <mml:mi>k<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>G<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    defined by\n                    <jats:italic>S<\/jats:italic>\n                    that are not induced by automorphisms of\n                    <jats:italic>G<\/jats:italic>\n                    . We also describe the group produced by all such 2-cuts of\n                    <jats:italic>G<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/s00373-025-03001-9","type":"journal-article","created":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T14:01:47Z","timestamp":1764770507000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Automorphisms of Token Graphs Generated by 2-cuts with the Same Neighbours"],"prefix":"10.1007","volume":"42","author":[{"given":"Ruy","family":"Fabila-Monroy","sequence":"first","affiliation":[]},{"given":"Sergio Gerardo","family":"G\u00f3mez-Galicia","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Gregorio-Longino","sequence":"additional","affiliation":[]},{"given":"Teresa I.","family":"Hoekstra-Mendoza","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1138-1190","authenticated-orcid":false,"given":"Ana","family":"Trujillo-Negrete","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,3]]},"reference":[{"issue":"1","key":"3001_CR1","first-page":"37","volume":"16","author":"Y Alavi","year":"1991","unstructured":"Alavi, Y., Behzad, M., Erd\u0151s, P., Lick, D.R.: Double vertex graphs. J. Comb. Inf. Syst. Sci. 16(1), 37\u201350 (1991)","journal-title":"J. Comb. Inf. Syst. Sci."},{"issue":"3","key":"3001_CR2","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s00373-011-1055-9","volume":"28","author":"R Fabila-Monroy","year":"2012","unstructured":"Fabila-Monroy, R., Flores-Pe\u00f1aloza, D., Huemer, C., Hurtado, F., Urrutia, J., Wood, D.R.: Token graphs. Graphs and Comb. 28(3), 365\u2013380 (2012). https:\/\/doi.org\/10.1007\/s00373-011-1055-9","journal-title":"Graphs and Comb."},{"issue":"3","key":"3001_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40590-025-00723-x","volume":"31","author":"R Fabila-Monroy","year":"2025","unstructured":"Fabila-Monroy, R., Trujillo-Negrete, A.: On the automorphism group of token graphs of complete bipartite graphs. Bolet. de la Soc. Matem\u00e1tica Mexicana 31(3), 1\u201323 (2025). https:\/\/doi.org\/10.1007\/s40590-025-00723-x","journal-title":"Bolet. de la Soc. Matem\u00e1tica Mexicana"},{"key":"3001_CR4","unstructured":"Fabila-Monroy, R., Trujillo-Negrete, A.L.: Connected ($$C_4$$, Diamond)-free graphs are uniquely reconstructible from their token graphs. arXiv preprint arXiv:2207.12336 (2022)"},{"key":"3001_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic graph theory, graduate texts in mathematics","author":"C Godsil","year":"2001","unstructured":"Godsil, C., Royle, G.: Algebraic graph theory, graduate texts in mathematics, vol. 207. Springer-Verlag, New York (2001). https:\/\/doi.org\/10.1007\/978-1-4613-0163-9"},{"issue":"6","key":"3001_CR6","doi-asserted-by":"publisher","first-page":"1627","DOI":"10.22199\/issn.0717-6279-5954","volume":"42","author":"S Ibarra","year":"2023","unstructured":"Ibarra, S., Rivera, L.M.: The automorphism groups of some token graphs. Proyecciones (Antofagasta) 42(6), 1627\u20131651 (2023). https:\/\/doi.org\/10.22199\/issn.0717-6279-5954","journal-title":"Proyecciones (Antofagasta)"},{"key":"3001_CR7","unstructured":"Johns, G.L.: Generalized distance in graphs. Ph.D. thesis, Western Michigan University (1988). https:\/\/scholarworks.wmich.edu\/dissertations\/2180"},{"key":"3001_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4176-8","volume-title":"An introduction to the theory of groups, graduate texts in mathematics","author":"JJ Rotman","year":"1995","unstructured":"Rotman, J.J.: An introduction to the theory of groups, graduate texts in mathematics, vol. 148, 4th edn. Springer-Verlag, New York (1995). https:\/\/doi.org\/10.1007\/978-1-4612-4176-8","edition":"4"},{"key":"3001_CR9","unstructured":"Rudolph, T.: Constructing physically intuitive graph invariants. arXiv preprint arXiv:quant-ph\/0206068 (2002)"},{"key":"3001_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2023.127872","volume":"446","author":"J Zhang","year":"2023","unstructured":"Zhang, J., Zhou, J.X., Li, Y.T., Kwon, Y.S.: The automorphisms of 2-token graphs. Appl. Math. Comput. 446, 127872 (2023). https:\/\/doi.org\/10.1016\/j.amc.2023.127872","journal-title":"Appl. Math. Comput."},{"key":"3001_CR11","unstructured":"Zhu, B.W., Liu, J., Lick, D.R., Alavi, Y.: $$n$$-tuple vertex graphs. In: Proceedings of the Twenty-third Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1992), vol. 89, pp. 97\u2013106 (1992)"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-03001-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-025-03001-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-03001-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T06:04:59Z","timestamp":1770962699000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-025-03001-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,3]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["3001"],"URL":"https:\/\/doi.org\/10.1007\/s00373-025-03001-9","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,3]]},"assertion":[{"value":"25 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 December 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"1"}}