Pancyclicity of kk-ary nn-cube networks with faulty vertices and edges

A graph GG is said to be ff-fault pp-pancyclic if after removing ff faulty vertices and/or edges from GG, the resulting graph contains a cycle of every length from pp to ∣V(G)∣∣V(G)∣. In this paper, we consider one of the most popular networks which is named kk-ary nn-cube, and show that it is (2n−2)(2n−2)-fault kk-pancyclic if k≥3k≥3 is odd. Finally, an example shows that our result is best possible in some sense.