On 2-arc-transitive Cayley graphs of Abelian groups

Abstract

A 2-arc in a graph X is a sequence of three distinct vertices of graph X where the first two and the last two are adjacent. A graph X is 2-arc-transitive if its automorphism group acts transitively on the set of 2-arcs of X. Some properties of 2-arc-transitive Cayley graphs of Abelian groups are considered. It is also proved that the set of generators of a 2-arc-transitive Cayley graph of an Abelian group which is not a circulant contains no elements of odd order.