Connected cubic <Emphasis Type="Italic">s</Emphasis>-arc-regular Cayley graphs of finite nonabelian simple groups

A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two sufficient and necessary conditions for such graphs to be 1- or 2-arcregular are given and based on the conditions, several infinite families of 1- or 2-arc-regular cubic Cayley graphs of alternating groups are constructed. This work was supported by Guangxi Science Foundations (Grant No. 0832054) and Guangxi Postgraduate Education Innovation Research (Grant No. 2008105930701M102)