Folded crossed cube with five or more dimensions is not vertex-transitive

Kulasinghe and Bettayeb [Inform. Process. Lett. 53 (1995) 33-36] proved that the crossed cube CQ_n (a synonym called multiply twisted hypercube in that paper) fails to be vertex-transitive for n ≥ 5. In this paper, we study vertex-transitivity on folded crossed cubes FCQ_n and show that FCQ_n is vertex-transitive if and only if n ϵ {1, 2, 4}.