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On the Number of Fixed Points of Automorphisms of Vertex-Transitive Graphs

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Abstract

The main result of this paper is that, if Γ is a finite connected 4-valent vertex- and edge-transitive graph, then either Γ is part of a well-understood family of graphs, or every non-identity automorphism of Γ fixes at most 1/3 of the vertices. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1000, Ljubljana, Slovenia

    Primož Potočnik

  2. Institute of Mathematics Physics and Mechanics, Jadranska 19, SI-1000, Ljubljana, Slovenia

    Primož Potočnik

  3. Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Via Cozzi 55, 20125, Milano, Italy

    Pablo Spiga

Authors
  1. Primož Potočnik
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  2. Pablo Spiga
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Correspondence to Pablo Spiga.

Additional information

The first-named author gratefully acknowledges the support of the Slovenian Research Agency ARRS, core funding programme P1-0294 and research project J1-1691.

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Potočnik, P., Spiga, P. On the Number of Fixed Points of Automorphisms of Vertex-Transitive Graphs. Combinatorica 41, 703–747 (2021). https://doi.org/10.1007/s00493-020-4509-y

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  • DOI: https://doi.org/10.1007/s00493-020-4509-y

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