k-Pancyclicity of k-ary n-Cube Networks under the Conditional Fault Model

摘要

The k-ary n-cube is one of the most popular interconnection networks for parallel and distributed systems. We prove that a k-ary n-cube with at most in 5 faulty edges but where every vertex is incident with at least two healthy edges is k-pancyclic and bipancyclic for n ≥ 3 and odd k ≥ 3.