A kind of conditional fault tolerance of (n, k)-star graphs

A vertex subset F is a R"k-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 R"k-vertex-cut of G is the R"k-connectivity of G, denoted by @k^k(G). This parameter measures a kind of conditional fault tolerance of networks. This parameter measures a kind of conditional fault tolerance of networks. In this paper, we determine R"1-connectivity and R"2-connectivity of (n,k)-star graphs.

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