3-extra connectivity of 3-ary n-cube networks.

Let G be a connected graph and S be a set of vertices. 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 h-extra connectivity for h=1,2 of k-ary n-cubes are gotten by Hsieh and Chang (2012) [14] for k≥4 and Zhu et al. (2011) [20] for k=3. In this paper, we show that the h-extra connectivity of the 3-ary n-cubes for h=3 is equal to 8n−12, where n≥3.