Connectivity of Direct Products of Graphs

Abstract

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.