Large Digraphs with Small Diameter: A Voltage Assignment Approach

The theory of lifting voltage digraphs provides a useful tool for constructing large digraphs with specified properties from suitable small base digraphs endowed with an assignment of voltages (= elements of a finite group) on arcs.
We revisit the degree/diameter problem for digraphs from this new perspective and prove a general upper bound on the diameter of a lifted digraph in terms of properties of the base digraph and voltage assignment.
In addition, we demonstrate that all currently known largest vertex-transitive Cayley digraphs for semidirect products of groups can be described by means of a voltage assignment construction using simpler groups.