  The topology of an interconnection network can be modeled by a graph
$G=(V(G),E(G))$. The connectivity of graph $G$ is a parameter to measure the
reliability of corresponding network. Direct product is one important graph
product. This paper mainly focuses on the super connectedness of direct product
of graphs and cycles.
  The connectivity of $G$, denoted by $\kappa(G)$, is the size of a minimum
vertex set $S\subseteq V(G)$ such that $G-S$ is not connected or has only one
vertex. The graph $G$ is said to be super connected, simply super-$\kappa$, if
every minimum vertex cut is the neighborhood of a vertex with minimum degree.
The direct product of two graphs $G$ and $H$, denoted by $G\times H$, is the
graph with vertex set $V(G \times H) = V (G)\times V (H)$ and edge set $E(G
\times H) = \{(u_{1} ,v_{1} )(u_{2} ,v_{2} )|\ u_{1}u_{2} \in E(G), v_{1}v_{2}
\in E(H)\}$. In this paper, we give some sufficient conditions for direct
product $G\times C_{n}$ to be super connected, where $C_{n}$ is the cycle on
$n$ vertices. Furthermore, those sufficient conditions are best possible.
