# zbMATH — the first resource for mathematics

Semisymmetric cubic graphs of orders $$36p$$, $$36p^2$$. (English) Zbl 1391.05127
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
Full Text: