Let \(\kappa(G)\) be the connectivity of \(G\) and \(G \times H\) the direct product of \(G\) and \(H\). We prove that for any graphs \(G\) and \(K\), with \(n \geq 3\),\(\kappa(G \times K_n) = \min\{n\kappa(G), (n-1)\delta(G)\},\) which was conjectured by Guji and Vumar.