2021
DOI: 10.48550/arxiv.2106.06750
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On orders of automorphisms of vertex-transitive graphs

Primoz Potocnik,
Micael Toledo,
Gabriel Verret

Abstract: 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 ≤ 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 Γ, Γ ∼ … Show more

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Cited by 1 publication
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“…Investigations on the number of fixed points of graph automorphisms do have interesting applications. For instance, very recently Potočnik, Toledo and Verret [14] pivoting on the results in [11] have proved remarkable results on the cycle structure of general automorphisms of 3-valent vertex-transitive and 4-valent arc-transitive graphs.…”
Section: Introductionmentioning
confidence: 99%
“…Investigations on the number of fixed points of graph automorphisms do have interesting applications. For instance, very recently Potočnik, Toledo and Verret [14] pivoting on the results in [11] have proved remarkable results on the cycle structure of general automorphisms of 3-valent vertex-transitive and 4-valent arc-transitive graphs.…”
Section: Introductionmentioning
confidence: 99%