On edge transitive Cayley graphs of square-free order

Zai Ping Lu (Nankai University, China)

A characterization is given of connected edge transitive Cayley graphs of square-free order. It is then applied to characterize locally primitive Cayley graphs of square-free order, and to classify 2-arc transitive Cayley graphs of square-free order. A complete classification is given of connected edge transitive tetravalent Cayley graphs of  square-free order. The classification involves new constructions of edge transitive graphs, and shows that, with a few of  exceptions,a connected edge transitive tetravalent Cayley graphs of square-free order is  arc  or edge regular.