| Naslov: | On orders of automorphisms of vertex-transitive graphs |
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| Avtorji: | ID Potočnik, Primož (Avtor)
ID Toledo, Micael (Avtor)
ID Verret, Gabriel (Avtor) |
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| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0095895624000029
 PDF - Predstavitvena datoteka, prenos (573,20 KB)
MD5: AC65152D691832B4F4B1A64AC61488AE
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | In 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 $C$. |
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| Ključne besede: | graphs, automorphism groups, vertex-transitive, regular orbit, cubic, tetravalent |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.05.2024 |
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| Leto izida: | 2024 |
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| Št. strani: | str. 123-153 |
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| Številčenje: | Vol. 166 |
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| PID: | 20.500.12556/DiRROS-18208  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 0095-8956 |
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| DOI: | 10.1016/j.jctb.2024.01.001 |
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| COBISS.SI-ID: | 182607619 |
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| Datum objave v DiRROS: | 19.02.2024 |
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| Število ogledov: | 167 |
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| Število prenosov: | 55 |
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| Metapodatki: |     |
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