On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency-Reference-Cited by-同舟云学术

On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency

Published:2022-09-27 Issue:1 Volume:57 Page:329-348
ISSN:0925-9899
Container-title:Journal of Algebraic Combinatorics
language:en
Short-container-title:J Algebr Comb

Author:

Barbieri Marco^ORCID,Grazian Valentina^ORCID,Spiga Pablo^ORCID

Abstract

AbstractWe prove that, if

$$\varGamma $$

Γ is a finite connected 3-valent vertex-transitive, or 4-valent vertex- and edge-transitive graph, then either

$$\varGamma $$

Γ is part of a well-understood family of graphs, or every non-identity automorphism of

$$\varGamma $$

Γ fixes at most 1/3 of the edges. This answers a question proposed by Primož Potočnik and the third author.

Funder

Università degli Studi di Pavia

Publisher

Springer Science and Business Media LLC

Subject

Discrete Mathematics and Combinatorics,Algebra and Number Theory

Link

https://link.springer.com/content/pdf/10.1007/s10801-022-01176-5.pdf

Reference19 articles.

1. Biggs, N.: Algebraic Graph Theory, 2nd edn. Cambridge University Press, Cambridge (1993)

2. Gardiner, A., Praeger, C.E.: A characterization of certain families of 4 symmetric graphs. European J. Combin. 15, 383–397 (1994). https://doi.org/10.1006/eujc.1994.1042

3. Godsil, C., Royle, G.: Algebraic Graph Theory, Graduate Texts in Mathematics, vol. 207. Springer, New York (2001)

4. Jajcay, R., Potočnik, P., Wilson, S.: The Praeger–Xu graphs: cycle structures, maps and semitransitive orientations. Acta Math. Univ. Comenian. 88, 22–26 (2019)

5. Jajcay, R., Potočnik, P., Wilson, S.: On the cayleyness of Praeger–Xu graphs. J. Combin. Theory Ser. B 152, 55–79 (2022). https://doi.org/10.1016/j.jctb.2021.09.003

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Vertex-primitive digraphs with large fixity;Annali di Matematica Pura ed Applicata (1923 -);2024-04-12