On 3-extra connectivity of k-ary n-cubes

Abstract: Given a graph G, a non-negative integer h and a set of vertices S, the h-extra connectivity of G is the cardinality of a minimum set S such that G-S is disconnected and each component of G-S has at least h+1 vertices. The 2-extra connectivity of k-ary n-cube is gotten by Hsieh et al. in [Theoretical Computer Science, 443 (2012) 63-69]. In this paper, we obtained the h-extra connectivity of the k-ary n-cube networks for h=3.