Cycles Embedding on Folded Hypercubes with Faulty Nodes

Abstract

Let $FF_v$ be the set of faulty nodes in an $n$-dimensional folded hypercube $FQ_n$ with $|FF_v| ≤ n − 1$ and all faulty vertices are not adjacent to the same vertex. In this paper, we show that if $n ≥ 4,$ then every edge of $FQ_n − F F_v$ lies on a fault-free cycle of every even length from 6 to $2^n − 2|F F_v|.$