Fault tolerance in k-ary n-cube networks

The k-ary n-cube is one of the most commonly used interconnection topologies for parallel and distributed computing systems. Let f(n,m) be the minimum number of faulty nodes that make every (n−m)-dimensional subcube faulty in under node-failure models. In this paper, we prove that f(n,0)=1, f(n,1)=k for odd k≥3, f(n,n−1)=kn−1 for odd k≥3, and for odd k≥3.