Problem of the Week
Hilton Memorial Lecture
Cheryl Praeger's normal quotient method has made the study of certain families of finite graphs (for instance, s-arc transitive and locally s-arc transitive graphs) more approachable by dividing the problem into two parts:
(I) Study the “basic graphs,” those graphs in the family that are not covers of anything but “trivial” graphs;
(II) Study the covers of the basic graphs.
While (I) has been studied extensively, not much work has been done toward (II).
In this talk, I will discuss how voltage graphs can be used to find covers of graphs where certain symmetries “lift,” and specifically look at the problem of determining the locally 2-arc transitive covers of K2,3. I will also demonstrate how the software GAP can be applied to problems like this.