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

Marušič, Dragan

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)

MSC:

05C25

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

Keywords:

automorphism group; one-regular graphs; non-solvable group; Cayley graph