I have just finished reading the proofs for my paper `On finite edge-primitive and edge-quasiprimitive graphs’ with Cai Heng Li which has just been accepted in JCTB. This paper has been a long time in the making as Li and I started the work in 2002! Usually when I submit a paper to a journal I put a preprint up on my research web page but I should really start uploading them also to the arxiv so I have just done so and it is now available there.
A graph is called edge-primitive if its automorphism group acts primitively on the set of edges. Many famous graphs such as the Heawood graph, Tutte-Coxeter graph, Hoffman-Singleton graph and Higman-Sims graph are edge-primitive. The paper begins a systematic study of edge-primitive and edge-quasiprimitive graphs by analysing the possible actions on vertices and edges.