A construction of pseudo metacirculants

摘要

Metacirculants were introduced by Alspach and Parsons in 1982 and have been a rich source of various topics since then. It is known that every metacirculant is a split weak metacirculant (A graph is called (split) weak metacirculant if it has a vertex-transitive (split) metacyclic subgroup of automorphisms). We say that a split metacirculant is a pseudo metacirculant if it is not metacirculant. In this paper, an infinite family of pseudo metacirculants is constructed, and this provides a negative answer to Question A in Zhou and Zhou (2018). (C) 2020 Elsevier B.V. All rights reserved.