## A family of one-regular graphs of valency 4.(English)Zbl 0870.05030

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.

### MSC:

 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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