SEMINAR: Groups and Combinatorics Seminar: A non-classification theorem for 2-arc-transitive graphs

Time and place: 3pm Friday 13 March in Weatherburn LT.

Speaker: Luke Morgan (UWA)

Title: A non-classification theorem for 2-arc-transitive graphs.

Abstract: It would be great to have a classification of 2-arc-transitive graphs! Sadly, this is probably out of reach. However, there are many results on classifications of 2-arc-transitive graphs of certain orders, valencies, girth, etc... In this talk, I'll describe a recent result of Eric Swartz, Gabriel Verret and myself where we do something slightly different. Rather than classify all the possible graphs, we show that for fixed n and k, the family of 2-arc-transitive graphs of order kp^n is finite, with p a prime, once the valency is big enough (relative to n). So, our "non-classification" shows that the most interesting 2-arc-transitive graphs are those of small valency (relative to n).