On Cyclic-Vertex Connectivity of $\left(n,k\right)$-Star Graphs

A vertex subset F ⊆ V G is a cyclic vertex-cut of a connected graph G if G − F is disconnected and at least two of its components contain cycles. The cyclic vertex-connectivity κ c G is denoted as the cardinality of a minimum cyclic vertex-cut. In this paper, we show that the cyclic vertex-connectivity of the n , k -star network S n , k is κ c S n , k = n + 2 k − 5 for any integer n ≥ 4 and k ≥ 2 .