Petersen type n-circulant and weak metacirculant

摘要

In this paper, we extend the class of multilayer generalized Petersen graphs introduced in [J. Combin. Theory Ser. A 155 (2018) 225–243] to a class of Petersen type n-circulants. We give a characterization of G-vertex-transitive Petersen type n-circulants Γ of odd prime power order and smallest possible valency, where G ≤  Aut (Γ) is a metacyclic group. As a result, we construct a class of non-Cayley graphs which have a vertex-transitive non-split metacyclic group of automorphisms. This corrects an error in the literature regarding weak metacirculants.