Semiregular automorphisms of edge-transitive graphs

Michael Giudici; P. Potočnik; Gabriel Verret

doi:10.1007/s10801-014-0515-8

Semiregular automorphisms of edge-transitive graphs

Michael Giudici, P. Potočnik, Gabriel Verret

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Abstract

The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism: a non-trivial automorphism whose cycles all have the same length. In this paper, we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.

Original language	English
Pages (from-to)	961-972
Journal	Journal of Algebraic Combinatorics
Volume	40
Issue number	4
Early online date	28 Mar 2014
DOIs	https://doi.org/10.1007/s10801-014-0515-8
Publication status	Published - Dec 2014

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abstract = "The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism: a non-trivial automorphism whose cycles all have the same length. In this paper, we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.",

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AB - The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism: a non-trivial automorphism whose cycles all have the same length. In this paper, we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.

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