Marušič, Dragan A family of one-regular graphs of valency 4. (English) Zbl 0870.05030 Eur. J. Comb. 18, No. 1, 59-64 (1997). A graph is said to be one-regular if its automorphism group acts regularly on the set of its arcs. This paper is concerned with one-regular graphs of valency 4. The author presents a construction for an infinite family of one-regular graphs of valency 4 with vertex stabilizer \(\mathbb{Z}_2\times \mathbb{Z}_2\) and a non-solvable group of automorphisms. In particular, for each alternating group \(A_n\), \(n\geq 5\) odd, a Cayley graph with one-regular automorphism group \(S_n\times \mathbb{Z}_2\) is constructed. Reviewer: U.Baumann (Dresden) Cited in 24 Documents MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:automorphism group; one-regular graphs; non-solvable group; Cayley graph PDF BibTeX XML Cite \textit{D. Marušič}, Eur. J. Comb. 18, No. 1, 59--64 (1997; Zbl 0870.05030) Full Text: DOI Link OpenURL