Revisiting the Comellas–Fiol–Gómez constructions of large digraphs of given degree and diameter

We analyze three constructions of Comellas and Fiol [F. Commellas, M.A. Fiol, Vertex-symmetric digraphs with small diameter, Discrete Applied Mathematics 58 (1995) 1–11] that produce large digraphs of given diameter and degree from smaller starter digraphs. We show that these constructions preserve coverings in the sense that if the starter digraph is a regular lift (in particular, a Cayley digraph), then the resulting digraph has the same property.