Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111254
Title: Automorphisms of a Distance-Regular Graph with Intersection Array {30,22,9;1,3,20}
Other Titles: Автоморфизмы дистанционно регулярного графа с массивом пересечений {30, 22, 9; 1, 3, 20}
Authors: Efimov, K. S.
Makhnev, A. A.
Issue Date: 2020
Publisher: Krasovskii Institute of Mathematics and Mechanics
Krasovskii Institute of Mathematics and Mechanics UB RAS
Citation: Efimov 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.
Abstract: A 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.
Keywords: GRAPH AUTOMORPHISM
SHILLA GRAPH
URI: http://hdl.handle.net/10995/111254
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85095685665
PURE ID: 13944861
ISSN: 0134-4889
metadata.dc.description.sponsorship: Funding 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).
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