Distance-regular graphs with primitive automorphism groups - Robert Bailey

Title: Distance-regular graphs with primitive automorphism groups

Abstract: Many well-known examples of distance-regular graphs (both infinite families and sporadic examples) arise from primitive permutation groups (e.g. Johnson, Hamming and Grassmann graphs).  Through the work of many authors, there are libraries of primitive groups on up to 4095 points available in the GAP and MAGMA computer algebra systems.  With the assistance of my undergraduate research students, I have been analysing these libraries, using the GRAPE package in GAP, with the ultimate aim of classifying the distance-regular (and strongly regular) graphs with such groups as automorphism groups.  In this talk, I will discuss the status of this work, a few surprises which came up along the way, and some (theoretical and computational) questions which remain open.