Conditional Fault-tolerant Cycles in Folded Hypercubes With Faulty Elements

As an attractive variation of the hypercubes Q(n), n -dimensional folded hypercube FQ(n) can be obtained by adding 2(n+1) complementary edges between the vertices of hypercube. Let FFv, (respectively, FPe) denotes the set of faulty vertices (respectively, faulty edges) in an n -dimensional folded hypercube. In this paper, we prove that FQ(n)-FFv-FFe, contains a fault-free cycle of length at least 2(n) -vertical bar FFv vertical bar if FQ(n) satisfies both of the constraints that (1) each vertex in FQ(n) is incident to at least two fault-free edges (2) vertical bar FFe vertical bar+vertical bar FFv vertical bar <= 2n-3, when n >= 4.