Abstract
Let Γ be an edge-symmetric distance-regular covering of a clique. Then the group G = Aut(Γ) acts twice transitively on the set Σ of antipodal classes. We propose a classification for the graphs based on the description of twice transitive permutation groups. This program is realized for a 1 = c 2. In this article we classify graphs in the case when the action of G on Σ is affine.
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Original Russian Text Copyright © 2013 Makhnev A.A., Paduchikh D.V., and Tsiovkina L.Yu.
The authors were supported by the Russian Foundation for Basic Research (Grant 12-01-00012), the RFBRNSFC (Grant 12-01-91155), the Program of the Division of Mathematical Sciences of the Russian Academy of Sciences (Grant 12-T-1-1003), and the Joint Program of the Ural and Siberian Divisions of the Russian Academy of Sciences (Grant 12-C-1-1018) with the National Academy of Sciences of Belarus (Grant 12-C-1-1009).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 6, pp. 1353–1367, November–December, 2013.
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Makhnev, A.A., Paduchikh, D.V. & Tsiovkina, L.Y. Edge-symmetric distance-regular coverings of cliques: The affine case. Sib Math J 54, 1076–1087 (2013). https://doi.org/10.1134/S0037446613060141
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DOI: https://doi.org/10.1134/S0037446613060141