# A Note on Constructing Large Cayley Graphs of Given Degree and Diameter by Voltage Assignments

### Abstract

Voltage graphs are a powerful tool for constructing large graphs (called *lifts*) with prescribed properties as covering spaces of small *base* graphs. This makes them suitable for application to the *degree/diameter problem*, which is to determine the largest order of a graph with given degree and diameter.

Many currently known largest graphs of degree $\le 15$ and diameter $\le 10$ have been found by computer search among Cayley graphs of semidirect products of cyclic groups. We show that *all* of them can in fact be described as lifts of smaller Cayley graphs of cyclic groups, with voltages in (other) cyclic groups. This opens up a new possible direction in the search for large vertex-transitive graphs of given degree and diameter.