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

Let G be a graph. Then T subset of V(G) is called an R(k)-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 R(k)-vertex-cut is the R(k)-vertex-connectivity of G and is denoted by kappa(k)(G). In this paper, we determine the numbers kappa(1) and kappa(2) for Cayley graphs generated by 2-trees, including the popular alternating group graphs. (C) 2011 Elsevier Inc. All rights reserved