Cycles embedding in folded hypercubes with conditionally faulty vertices

A network is said to be conditionally faulty if its every vertex is incident to at least g fault-free vertices, where g >= 1. An n-dimensional folded hypercube FQ(n) is a well-known variation of an n-dimensional hypercube Q(n), which can be constructed from Q(n), by adding an edge to every pair of vertices with complementary addresses. In this paper, we define that a network is said to be g-conditionally faulty if its every vertex is incident to at least g fault-free vertices. Then, let FFv, denote the set of faulty vertices in FQ(n), we consider the cycles embedding properties in 4-conditionally faulty FQ(n) - FFv, as follows: 1. For n >= 3, FQ(n), FFv contains a fault-free cycle of every even length from 4 to 2(n) - 2 vertical bar FFv (vertical bar), where vertical bar FFv vertical bar <= 2n - 5; 2. For even n >= 4, FQ(n) - FFv, contains a fault-free cycle of every odd length from n + 1 to 2(n) - 2 vertical bar FFv (vertical bar) - 1, where vertical bar FFv vertical bar <= 2n - 5. (C) 2016 Elsevier B.V. All rights reserved.