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Automorphism Groups of Small Distance-Regular Graphs

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Algebra and Logic Aims and scope

We consider undirected graphs without loops and multiple edges. Previously, V. P. Burichenko and A. A. Makhnev [1] found intersection arrays of distance-regular locally cyclic graphs with the number of vertices at most 1000. It is shown that the automorphism group of a graph with intersection array {15, 12, 1; 1, 2, 15}, {35, 32, 1; 1, 2, 35}, {39, 36, 1; 1, 2, 39}, or {42, 39, 1; 1, 3, 42} (such a graph enters the above-mentioned list) acts intransitively on the set of its vertices.

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References

  1. V. P. Burichenko and A. A. Makhnev “On amply regular locally cyclic graphs,” Modern Problems in Mathematics, Proc. 42nd All-Russian School–Conference of Young Scientists, Institute of Mathematics and Mechanics, UB RAS, Yekaterinburg (2011), pp. 181-183.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Ekaterinburg, 620990, Russia

    I. N. Belousov

  2. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Ekaterinburg, 620990, Russia

    A. A. Makhnev

Authors
  1. I. N. Belousov
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  2. A. A. Makhnev
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Correspondence to I. N. Belousov.

Additional information

Supported by Russian Science Foundation, project No. 14-11-00061.

Translated from Algebra i Logika, Vol. 56, No. 4, pp. 395-405, July-August, 2017.

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Belousov, I.N., Makhnev, A.A. Automorphism Groups of Small Distance-Regular Graphs. Algebra Logic 56, 261–268 (2017). https://doi.org/10.1007/s10469-017-9447-4

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  • DOI: https://doi.org/10.1007/s10469-017-9447-4

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