Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111254
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dc.contributor.authorEfimov, K. S.en
dc.contributor.authorMakhnev, A. A.en
dc.date.accessioned2022-05-12T08:15:25Z-
dc.date.available2022-05-12T08:15:25Z-
dc.date.issued2020-
dc.identifier.citationEfimov K. S. Automorphisms of a Distance-Regular Graph with Intersection Array {30,22,9;1,3,20} [Автоморфизмы дистанционно регулярного графа с массивом пересечений {30, 22, 9; 1, 3, 20}] / K. S. Efimov, A. A. Makhnev // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 3. — P. 23-31.en
dc.identifier.issn0134-4889-
dc.identifier.otherAll Open Access, Bronze3
dc.identifier.urihttp://hdl.handle.net/10995/111254-
dc.description.abstractA distance-regular graph Γ of diameter 3 is called a Shilla graph if it has the second eigenvalue θ1 = a3. In this case a = a3 divides k and we set b = b(Γ) = k/a. Koolen and Park obtained the list of intersection arrays for Shilla graphs with b = 3. There exist graphs with intersection arrays {12, 10, 5; 1, 1, 8} and {12, 10, 3; 1, 3, 8}. The nonexistence of graphs with intersection arrays {12, 10, 2; 1, 2, 8}, {27, 20, 10; 1, 2, 18}, {42, 30, 12; 1, 6, 28}, and {105, 72, 24; 1, 12, 70} was proved earlier. In this paper we study the automorphisms of a distance-regular graph Γ with intersection array {30, 22, 9; 1, 3, 20}, which is a Shilla graph with b = 3. Assume that a is a vertex of Γ, G = Aut(Γ) is a nonsolvable group, G¯ = G/S(G), and T¯ is the socle of G¯. Then T¯ ∼= L2(7), A7, A8, or U3(5). If Γ is arc-transitive, then T is an extension of an irreducible F2U3(5)-module V by U3(5) and the dimension of V over F3 is 20, 28, 56, 104, or 288. © 2020 Sverre Raffnsoe. All rights reserved.en
dc.description.sponsorshipFunding Agency: This work was supported by the Russian Foundation for Basic Research - the National Natural Science Foundation of China (project no. 20-51-53013_a).en
dc.format.mimetypeapplication/pdfen
dc.language.isoroen
dc.publisherKrasovskii Institute of Mathematics and Mechanicsen1
dc.publisherKrasovskii Institute of Mathematics and Mechanics UB RASen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceTr. Inst. Mat. Meh. UrO RAN2
dc.sourceTrudy Instituta Matematiki i Mekhaniki UrO RANen
dc.subjectGRAPH AUTOMORPHISMen
dc.subjectSHILLA GRAPHen
dc.titleAutomorphisms of a Distance-Regular Graph with Intersection Array {30,22,9;1,3,20}en
dc.title.alternativeАвтоморфизмы дистанционно регулярного графа с массивом пересечений {30, 22, 9; 1, 3, 20}ru
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.scopus85095685665-
local.contributor.employeeEfimov, K.S., Ural State University of Economics, Yekaterinburg, 620144, Russian Federation; Makhnev, A.A., Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108, Russian Federation, Ural Federal University, Yekaterinburg, 620083, Russian Federationen
local.description.firstpage23-
local.description.lastpage31-
local.issue3-
local.volume26-
local.contributor.departmentUral State University of Economics, Yekaterinburg, 620144, Russian Federation; Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108, Russian Federation; Ural Federal University, Yekaterinburg, 620083, Russian Federationen
local.identifier.pure13944861-
local.identifier.eid2-s2.0-85095685665-
local.fund.rffi20-51-53013
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