Folded hypercubes with cycles embedding in hybrid conditionally faulty

A network is defined as g-conditionally faulty if there are g fault-free neighbors is found in every vertex at least, where g >= 1. An folded hypercube FQn with n-dimension, a famous variation of an n-dimensional hypercube Qn, can be established from Qn through putting in an edge to every pair of vertices which has complementary addresses. Any odd n for FQn is bipartite. Let FFv represents the faulty vertex set and FFe represents the faulty edge set in FQn, as well as let FFQn(e) represents the faulty vertex and/or faulty edge set which is incident to the end-vertices of any edge e belongs to E(FQn). Suppose that FQn is 4-conditionally faulty and |FFv| + |FFe| <= 2n - 7. We prove the properties of embedding fault-tolerant cycles in FQn - FFv - FFe as follows: 1. For n >= 4 and |FFQn(e)| <= n - 2, FQn - FFv - FFe consists of the fault-free cycle for every even length from 4 to 2^n – 2|FFv|; 2. For n = 4 and n >= 8 where n is even, and |FFQn(e)| <= n - 3, FQn - FFv - FFe consists of the fault-free cycle for every odd length from n + 1 to 2^n – 2|FFv| - 1. This study has been submitted to HAL an open archive for the sustainability (https://hal.archives-ouvertes.fr/hal-01579266v2).