Originators: ???? (presented by A. Kostochka - REGS 2009)
Definitions: A graph G is edge-transitive if, for any two edges e and e', there is an automorphism of G that takes the set of endpoints of e into the set of endpoints of e'.
Question: What is the maximum diameter among 3-regular edge-transitive graphs?
Comments: There are 4-regular edge-transitive graphs whose diameter is linear in the number of vertices, but for degreee 3 the best that is known is a multiple of √n. This is counterintuitive, since a 4-regular graph with n vertices has more edges than a 3-regular graph. A 4-regular example is the graph obtained from a cycle by expanding each vertex into an independent set of size 2.