A kind of conditional fault tolerance of alternating group graphs

A vertex subset F is a k-restricted vertex-cut of a connected graph G if G-F is disconnected and every vertex in G-F has at least k good neighbors in G-F. The cardinality of the minimum k-restricted vertex-cut of G is the k-restricted connectivity of G, denoted by @k^k(G). This parameter measures a kind of conditional fault tolerance of networks. In this paper, we show that for the n-dimensional alternating group graph AG"n, @k^2(AG"4)=4 and @k^2(AG"n)=6n-18 for n>=5.