Semiregular automorphisms of edge-transitive graphs

2013/06/09 by Michael Giudici, Primoz Potocnik, Primož Potočnik +4
Computer Science · Mathematics · #Advanced Graph Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.1306.1971

arxiv created 2013/06/09 · openalex publication_date 2013/06/09 · arxiv updated 2013/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism, that is, a nontrivial 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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