On Cyclic-Vertex Connectivity of n , k -Star Graphs

Abstract

A vertex subset $F\subseteq V\left(G\right)$ 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 ${\kappa }_c\left(G\right)$ is denoted as the cardinality of a minimum cyclic vertex-cut. In this paper, we show that the cyclic vertex-connectivity of the $\left(n,k\right)$ -star network $S_{n,k}$ is ${\kappa }_c\left(S_{n,k}\right)=n+2k-5$ for any integer $n\ge 4$ and $k\ge 2$ .