{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T02:02:54Z","timestamp":1784685774511,"version":"3.55.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T00:00:00Z","timestamp":1781740800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T00:00:00Z","timestamp":1781740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12471022"],"award-info":[{"award-number":["12471022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271524"],"award-info":[{"award-number":["12271524"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271527"],"award-info":[{"award-number":["12271527"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2022JJ30674"],"award-info":[{"award-number":["2022JJ30674"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1007\/s10623-026-01884-0","type":"journal-article","created":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T12:16:15Z","timestamp":1781784975000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On s-flag-transitive designs and semisymmetric graphs"],"prefix":"10.1007","volume":"94","author":[{"given":"Zheng","family":"Huang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2396-637X","authenticated-orcid":false,"given":"Weijun","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qian-Fen","family":"Liao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li-Hua","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Jin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,18]]},"reference":[{"key":"1884_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139507660","volume-title":"Design Theory","author":"T Beth","year":"1999","unstructured":"Beth T., Jungnickel D., Lenz H.: Design Theory, vol. 1\u20132, 2nd edn Cambridge University Press, Cambridge (1999).","edition":"2"},{"key":"1884_CR2","volume-title":"Algebraic Graph Theory","author":"N Biggs","year":"1993","unstructured":"Biggs N.: Algebraic Graph Theory, 2nd edn Cambridge University Press, Cambridge (1993).","edition":"2"},{"key":"1884_CR3","doi-asserted-by":"publisher","first-page":"533","DOI":"10.4153\/CMB-1968-063-0","volume":"11","author":"IZ Bouwer","year":"1968","unstructured":"Bouwer I.Z.: On edge but not vertex transitive cubic graphs. Can. Math. Bull. 11, 533\u2013535 (1968).","journal-title":"Can. Math. Bull."},{"key":"1884_CR4","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/0095-8956(72)90030-5","volume":"12","author":"IZ Bouwer","year":"1972","unstructured":"Bouwer I.Z.: On edge but not vertex transitive regular graphs. J. Comb. Theory B 12, 32\u201340 (1972).","journal-title":"J. Comb. Theory B"},{"key":"1884_CR5","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/0097-3165(88)90056-8","volume":"49","author":"F Buekenhout","year":"1988","unstructured":"Buekenhout F., Delandtsheer A., Doyen J.: Finite linear spaces with flag-transitive groups. J. Comb. Theory A 49, 268\u2013293 (1988).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR6","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/BF00181466","volume":"36","author":"F Buekenhout","year":"1990","unstructured":"Buekenhout F., Delandtsheer A., Doyen J., Kleidman P.B., Liebeck M.W., Saxl J.: Linear spaces with flag-transitive automorphism groups. Geom. Dedicata 36, 89\u201394 (1990).","journal-title":"Geom. Dedicata"},{"key":"1884_CR7","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/0097-3165(89)90052-6","volume":"51","author":"AR Camina","year":"1989","unstructured":"Camina A.R., Siemons J.: Block transitive automorphism group of $$2$$-$$(v, k,1)$$ block designs. J. Comb. Theory A 51, 268\u2013276 (1989).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR8","doi-asserted-by":"crossref","unstructured":"Delandtsheer A.: Finite flag-transitive linear spaces with alternating socle. In: Algebraic Combinatorics and Applications (G\u00f6\u00dfweinstein, 1999), pp. 79\u201388. Springer. Berlin (2001).","DOI":"10.1007\/978-3-642-59448-9_5"},{"key":"1884_CR9","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/0097-3165(86)90033-6","volume":"43","author":"A Delandtsheer","year":"1986","unstructured":"Delandtsheer A., Doyen J., Siemons J., Tamburini C.: Doubly homogeneous $$2$$-$$(v, k,1)$$ designs. J. Comb. Theory A 43, 140\u2013145 (1986).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR10","volume-title":"Linear Groups with an Exposition of the Galois Field Theory, Teubner, Leipzig, 1901: Reprint","author":"LE Dickson","year":"1958","unstructured":"Dickson L.E.: Linear Groups with an Exposition of the Galois Field Theory, Teubner, Leipzig, 1901: Reprint. Dover Publications, New York (1958)."},{"key":"1884_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0731-3","volume-title":"Permutation Groups, GTM","author":"JD Dixon","year":"1996","unstructured":"Dixon J.D., Mortimer B.: Permutation Groups, GTM, vol. 163. Springer, New York (1996)."},{"key":"1884_CR12","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10801-014-0536-3","volume":"41","author":"SF Du","year":"2015","unstructured":"Du S.F., Wang L.: A classification of semisymmetric graphs of order $$2p^3$$: unfaithful case. J. Algebr. Comb. 41, 275\u2013302 (2015).","journal-title":"J. Algebr. Comb."},{"key":"1884_CR13","doi-asserted-by":"publisher","first-page":"2685","DOI":"10.1080\/00927870008826987","volume":"28","author":"SF Du","year":"2000","unstructured":"Du S.F., Xu M.Y.: A classification of semisymmetric graphs of order $$2pq$$. Commun. Algebra 28, 2685\u20132715 (2000).","journal-title":"Commun. Algebra"},{"key":"1884_CR14","doi-asserted-by":"publisher","first-page":"4031","DOI":"10.1016\/j.disc.2007.07.096","volume":"308","author":"YQ Feng","year":"2008","unstructured":"Feng Y.Q., Zhou J.X.: Semisymmetric graphs. Discret. Math. 308, 4031\u20134035 (2008).","journal-title":"Discret. Math."},{"key":"1884_CR15","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0021-9800(67)80069-3","volume":"3","author":"J Folkman","year":"1967","unstructured":"Folkman J.: Regular line-symmetric graphs. J. Comb. Theory B 3, 215\u2013232 (1967).","journal-title":"J. Comb. Theory B"},{"key":"1884_CR16","first-page":"591","volume":"48","author":"N Gill","year":"2007","unstructured":"Gill N.: $$\\rm PSL (3, q)$$ and line-transitive linear spaces. Beitr. Algebra Geom. 48, 591\u2013620 (2007).","journal-title":"Beitr. Algebra Geom."},{"key":"1884_CR17","doi-asserted-by":"publisher","first-page":"2579","DOI":"10.1007\/s11425-012-4424-9","volume":"55","author":"H Han","year":"2012","unstructured":"Han H., Lu Z.P.: Semisymmetric graphs of order $$6p^2$$ and prime valency. Sci. China Math. 55, 2579\u20132592 (2012).","journal-title":"Sci. China Math."},{"key":"1884_CR18","doi-asserted-by":"publisher","first-page":"2671","DOI":"10.1007\/s11425-015-5022-4","volume":"58","author":"H Han","year":"2015","unstructured":"Han H., Lu Z.P.: Semisymmetric graphs admitting primitive groups of degree $$9p$$. Sci. China Math. 58, 2671\u20132682 (2015).","journal-title":"Sci. China Math."},{"key":"1884_CR19","unstructured":"Harary F., Dauber E.: Line-symmetric but not point-symmetric graphs (Unpublished)."},{"key":"1884_CR20","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1515\/advg.2005.5.2.195","volume":"5","author":"M Huber","year":"2005","unstructured":"Huber M.: The classification of flag-transitive Steiner 3-designs. Adv. Geom. 5, 195\u2013221 (2005).","journal-title":"Adv. Geom."},{"key":"1884_CR21","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s10801-006-0053-0","volume":"26","author":"M Huber","year":"2007","unstructured":"Huber M.: The classification of flag-transitive Steiner 4-designs. J. Algebr. Comb. 26, 183\u2013207 (2007).","journal-title":"J. Algebr. Comb."},{"key":"1884_CR22","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s10801-007-0065-4","volume":"26","author":"M Huber","year":"2007","unstructured":"Huber M.: A census of highly symmetric combinatorial designs. J. Algebr. Comb. 26, 453\u2013476 (2007).","journal-title":"J. Algebr. Comb."},{"key":"1884_CR23","first-page":"123","volume":"12","author":"M Huber","year":"2010","unstructured":"Huber M.: On the existence of block-transitive combinatorial designs. Discret. Math. Theor. Comput. Sci. 12, 123\u2013132 (2010).","journal-title":"Discret. Math. Theor. Comput. Sci."},{"key":"1884_CR24","unstructured":"Iofinova M.E., Ivanov A.A.: Biprimitive cubic graphs, investigation in algebraic theory of combinatorial objects. In: Proceedings of the Seminar, 1985, pp. 124\u2013134. Institute for System Studies, Moscow (1985)."},{"key":"1884_CR25","first-page":"273","volume":"34","author":"AV Ivanov","year":"1987","unstructured":"Ivanov A.V.: On edge but not vertex transitive regular graphs. Ann. Discret. Math. 34, 273\u2013286 (1987).","journal-title":"Ann. Discret. Math."},{"key":"1884_CR26","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/0097-3165(85)90022-6","volume":"38","author":"WM Kantor","year":"1985","unstructured":"Kantor W.M.: Homogeneous designs and geometric lattices. J. Comb. Theory A 38, 66\u201374 (1985).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR27","doi-asserted-by":"crossref","unstructured":"Kleidman P.B.: The finite flag-transitive linear spaces with an exceptional automorphism group. In: Finite Geometries and Combinatorial Designs. Contemporary Mathematics, vol. 111, pp. 117\u2013136. American Mathematical Society, Providence (1990).","DOI":"10.1090\/conm\/111\/1079743"},{"key":"1884_CR28","first-page":"399","volume":"25","author":"MH Klin","year":"1981","unstructured":"Klin M.H.: On edge but not vertex transitive regular graphs. Colloq. Math. Soc. J. Bolyai Algebr. Methods Graph Theory Szeged 1978 25, 399\u2013403 (1981).","journal-title":"Colloq. Math. Soc. J. Bolyai Algebr. Methods Graph Theory Szeged 1978"},{"key":"1884_CR29","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1006\/jcta.2000.3067","volume":"93","author":"HL Li","year":"2001","unstructured":"Li H.L., Liu W.J.: Solvable block-transitive automorphism groups of $$2$$-$$(v, k,1)$$ designs. J. Comb. Theory A 93, 182\u2013191 (2001).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR30","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1006\/jcta.1998.2897","volume":"84","author":"MW Liebeck","year":"1998","unstructured":"Liebeck M.W.: The classification of finite linear spaces with flag-transitive automorphism groups of affine type. J. Comb. Theory A 84, 196\u2013235 (1998).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR31","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/S0097-3165(03)00013-X","volume":"103","author":"WJ Liu","year":"2003","unstructured":"Liu W.J.: Finite linear spaces admitting a two-dimensional projective linear group. J. Comb. Theory A 103, 209\u2013222 (2003).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR32","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/BF01112361","volume":"90","author":"D Livingstong","year":"1965","unstructured":"Livingstong D., Wagner A.: Transitivity of finite permutation groups on unordered sets. Math. Z. 90, 393\u2013403 (1965).","journal-title":"Math. Z."},{"key":"1884_CR33","first-page":"193","volume":"1","author":"CE Praeger","year":"1990","unstructured":"Praeger C.E.: Block-transitive designs and maximal subgroups of finite symmetric groups. Australas. J. Comb. 1, 193\u2013205 (1990).","journal-title":"Australas. J. Comb."},{"key":"1884_CR34","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1006\/jcta.2002.3305","volume":"100","author":"J Saxl","year":"2002","unstructured":"Saxl J.: On finite linear spaces with almost simple flag-transitive automorphism groups. J. Comb. Theory A 100, 322\u2013348 (2002).","journal-title":"J. Comb. Theory A"},{"key":"1884_CR35","unstructured":"The GAP Group: GAP\u2014Group, Algorithms, and Programming, Version 4.11.0. The GAP Group (2022). https:\/\/www.gap-system.org."},{"key":"1884_CR36","unstructured":"Titov V.K.: On symmetry in the graphs, Voprocy Kibernetiki. In: Proceedings of the II All Union Seminar on Combinatorial Mathematics, Part 2, vol. 15, pp. 76\u2013109. Nauka, Moscow (1975)."},{"key":"1884_CR37","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/S0012-365X(03)00048-7","volume":"271","author":"S Wilson","year":"2003","unstructured":"Wilson S.: A worthy family of semisymmetric graphs. Discret. Math. 271, 283\u2013294 (2003).","journal-title":"Discret. Math."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01884-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-026-01884-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01884-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T01:41:18Z","timestamp":1784684478000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-026-01884-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,18]]},"references-count":37,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["1884"],"URL":"https:\/\/doi.org\/10.1007\/s10623-026-01884-0","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,18]]},"assertion":[{"value":"16 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 December 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 June 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare they have no financial interests.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"141"}}