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

• We investigate the structure of 3-ary n  -cubes Qn3 after deleting vertices.
• We prove that the κ3(Qn3)=8n−12 for n≥3n≥3.
• The previous best result by Zhu et al. about κ2(Qn3) is generalized to κ3(Qn3).

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−SG−S is disconnected and each component of G−SG−S has at least h+1h+1 vertices. The h  -extra connectivity for h=1,2h=1,2 of k-ary n-cubes are gotten by Hsieh and Chang (2012) [14] for k≥4k≥4 and Zhu et al. (2011) [20] for k=3k=3. In this paper, we show that the h-extra connectivity of the 3-ary n  -cubes for h=3h=3 is equal to 8n−128n−12, where n≥3n≥3.