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On orders of automorphisms of vertex-transitive graphsPotočnik, Primož, 1971- ; Toledo, Micael, matematik ; Verret, GabrielIn this paper we investigate orders, longest cycles and the number of cycles of automorphisms of finite vertex-transitive graphs. In particular, we show that the order of every automorphism of a ... connected vertex-transitive graph with ▫$n$▫ vertices and of valence ▫$d$▫, ▫$d\le 4$▫, is at most ▫$c_d n$▫ where ▫$c_3=1$▫ and ▫$c_4 = 9$▫. Whether such a constant ▫$c_d$▫ exists for valencies larger than ▫$4$▫ remains an unanswered question. Further, we prove that every automorphism ▫$g$▫ of a finite connected ▫$3$▫-valent vertex-transitive graph ▫$\Gamma$▫, ▫$\Gamma \not\cong K_{3,3}$▫, has a regular orbit, that is, an orbit of ▫$\langle g \rangle$▫ of length equal to the order of ▫$g$▫. Moreover, we prove that in this case either ▫$\Gamma$▫ belongs to a well understood family of exceptional graphs or at least ▫$5/12$▫ of the vertices of ▫$\Gamma$▫ belong to a regular orbit of ▫$g$▫. Finally, we give an upper bound on the number of orbits of a cyclic group of automorphisms ▫$C$▫ of a connected ▫$3$▫-valent vertex-transitive graph ▫$\Gamma$▫ in terms of the number of vertices of ▫$\Gamma$▫ and the length of a longest orbit of ▫$C$▫.Source: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 166, May 2024, str. 123-153)Type of material - article, component part ; adult, seriousPublish date - 2024Language - englishCOBISS.SI-ID - 182607619
Author
Potočnik, Primož, 1971- |
Toledo, Micael, matematik |
Verret, Gabriel
Topics
graphs |
automorphism groups |
vertex-transitive |
regular orbit |
cubic |
tetravalent
Author | Potočnik, Primož, 1971- ; Toledo, Micael, matematik ; Verret, Gabriel |
Title | On orders of automorphisms of vertex-transitive graphs |
Publication date | 2024-05-01 |
COBISS.SI-ID | 182607619 |
Publication version in repository | Publisher's version |
Publication licence | Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International |
Embargo | Immediate publication for public |
Project(s) from which the publication was funded
Title | Acronym | Project ID | Funder |
---|---|---|---|
Računsko intenzivne metode v teoretičnem računalništvu, diskretni matematiki, kombinatorični optimizaciji ter numerični analizi in algebri z uporabo v naravoslovju in družboslovju | P1-0294-2020 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Weissova domneva in posplošitve | J1-1691-2019 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Generiranje, analiza in katalogizacija simetričnih grafov | J1-4351-2022 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
Files that belong to the publication
Link |
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https://www.sciencedirect.com/science/article/pii/S0095895624000029 |
https://dirros.openscience.si/IzpisGradiva.php?id=18208 |
https://repozitorij.uni-lj.si/IzpisGradiva.php?id=154511 |
source: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 166, May 2024, str. 123-153)
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Potočnik, Primož, 1971- | 18838 |
Toledo, Micael, matematik | 39104 |
Verret, Gabriel | 28586 |
Source: Personal bibliographies
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