A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

Let G be a graph. Then T ⊆ V(G) is called an Rk-vertex-cut if G − T is disconnected and each vertex in V(G) − T has at least k neighbors in G − T. The size of a smallest Rk-vertex-cut is the Rk-vertex-connectivity of G and is denoted by κk(G). In this paper, we determine the numbers κ1 and κ2 for Cayley graphs generated by 2-trees, including the popular alternating group graphs.