Cycles embedding in folded hypercubes with conditionally faulty vertices

Abstract

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 FQn is a well-known variation of an n-dimensional hypercube Qn, which can be constructed from Qn 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 FQn, we consider the cycles embedding properties in 4-conditionally faulty FQn−FFv, as follows: 1.For n≥3, FQn−FFv contains a fault-free cycle of every even length from 4 to 2n−2∣FFv∣, where |FFv|≤2n−5;2.For even n≥4, FQn−FFv contains a fault-free cycle of every odd length from n+1 to 2n−2∣FFv∣−1, where |FFv|≤2n−5.