Semisymmetric cubic graphs of orders \(36p\), \(36p^2\). (English) Zbl 1391.05127

Alaeiyan, Mehdi; Lashani, Mohsen; Hosseinipoor, M. K.

Filomat 27, No. 8, 1569-1573 (2013).

Summary: A cubic graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. The semisymmetric cubic graphs of orders \(6p\) and \(6p^2\) were classified in [S. Du and M. Xu, Commun. Algebra 28, No. 6, 2685–2715 (2000; Zbl 0944.05051)] and [Z. Lu et al., Sci. China, Ser. A 47, No. 1, 1–17 (2004; Zbl 1217.05107)], respectively. In this paper we first classify all connected cubic semisymmetric graphs of order \(36p\) for each prime \(p\) and also classify all connected cubic semisymmetric graphs of order \(36p^2\), where \(p\neq 5\) and \(7\) is a prime.

MSC:

05C25

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

Keywords:

regular cover; semisymmetric graph; semiregular subgroup