A kind of conditional vertex connectivity of star graphs

A subset F subset of V(G) is called an R-2-vertex-cut of G if G - F is disconnected and each vertex u epsilon V(G) - F has at least two neighbors in G - F. The cardinality, of a minimum R-2-vertex-cut of G, denoted by k(2) (G), is the R-2- vertex-connectivity of G. In this work, we prove that k(2)(S-n) = 6(n - 3) for n >= 4, where S-n is the n-dimensional star graph. (C) 2008 Elsevier Ltd. All rights reserved.