Distance-transitive graphs of valency five

If u and v are vertices of the (finite, connected) graph F, let d(u, v) denote the length of the shortest path joining u to v in F. The graph F is said to be distance-transitive if whenever d(u,v) = d(u',v'), there exists an automorphism g of F such that u = u' and if = v'. Distance-transitive graphs of valency 3 and 4 were originally classified [2, 11, 12, 13] by using a computer to generate all "feasible intersection arrays" (cf. [1, Chapter 20]). In both cases a classification has since been given by hand [4, 5]. We continue this latter tradition and prove the following theorem—which was recently proved independently by Ivanov et al. using a computer [10].