Cycles embedding on folded hypercubes with faulty nodes

摘要

Let F~(Fv) be the set of faulty nodes in an n-dimensional folded hypercube F~(Qn) with |F~(Fv)|≤n-2. In this paper, we show that if n≥3, then every edge of F~(Qn)-F~(Fv) lies on a fault-free cycle of every even length from 4 to 2~n-2|F~(Fv)|, and if n≥2 and n is even, then every edge of F~(Qn)-F~(Fv) lies on a fault-free cycle of every odd length from n+1 to 2~n- 2|F~(Fv)|-1.