Normal Edge-Transitive Cayley Graphs of Frobenius Groups

The Cayley Graph was introduced in the late 19th century as a means to study the structure of a group. Since then, the study of Cayley graphs has grown beyond this, and the field has applications in combinatorics, probability and computer science.

In studying Cayley graphs we attempt to identify small cases which may be considered `fundamental'. In 1999 Praeger identified the Normal Edge-Transitive Cayley Graphs as an important family for study, and provided a quotient operation allowing us to reduce their study to a family of small cases.

In my dissertation I solve an opposite problem: given a small normal edge-transitive Cayley graph, I determine all connected, normal edge-transitive Cayley graphs of a `second smallest' order, namely a product of two primes.