Extra connectivity measures of 3-ary n-cubes

The h-extra connectivity is an important parameter to measure the reliability and fault tolerance ability of large interconnection networks. The k-ary ncube is an important interconnection network of parallel computing systems. The 1-restricted connectivity of k-ary n-cubes has been obtained by Chen et al. for k ≥ 4 in [6]. Nevertheless, the h-extra connectivity of 3-ary ncubes has not been obtained yet. In this paper we prove that the 1-extra connectivity of 3-ary n-cube is 4n− 3 for n ≥ 2 and the 2-extra connectivity of 3-ary n-cube is 6n− 7 for n ≥ 3.