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 $n\ge 3$,$\kappa (G\times K_n)=min\{n\kappa (G),(n-1)\delta (G)\},$ which was conjectured by Guji and Vumar.