An infinite family of cubic edge- but not vertex-transitive graphs Original Research Article

An infinite family of cubic edge- but not vertex-transitive graphs is constructed. The graphs are obtained as regular Zn-covers of K3,3 where n=p1e1p2e2⋯pkek where pi are distinct primes congruent to 1 modulo 3, and ei⩾1. Moreover, it is proved that the Gray graph (of order 54) is the smallest cubic edge- but not vertex-transitive graph.