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 n-cube 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 > 3 in [Y.-C. Chen, J. J. M. Tan, Restricted connectivity for three families of interconnection networks, Applied Mathematics and Computation 188 (2) (2007)1848--1855]. Nevertheless, the h-extra connectivity of 3-ary n-cubes has not been obtained yet. In this paper we prove that the 1-extra connectivity of a 3-ary n-cube is 4n-3 for n> 1 and the 2-extra connectivity of 3-ary n-cube is 6n-7 for n> 2.