On the extraconnectivity ofk-aryn-cube networks

Given a graph G and a non-negative integer g, the g-extraconnectivity of G is the cardinality of a minimum set of vertices in G, if such a set exists, whose deletion disconnects G and leaves every remaining component with more than g vertices. The 2-extraconnectivity of k-ary n-cubes is gotten by Hsieh and Chang [Extraconnectivity of k-ary n-cube networks. Theoret. Comput. Sci. 443 (2012) 63–69] for k≥4. This paper shows that the 3-extraconnectivity of the k-ary n-cubes is 8n−9, where n≥3 and k≥4.