Reliability measures in relation to the h-extra edge-connectivity of folded hypercubes

Abstract

The folded hypercube FQn, as a variation of the hypercube Qn, was proposed by A. El-Amawy and S. Latifi in 1991. The h-extra edge-connectivity of the underlying topological graph of a multiprocessor system is a kind of measure for the reliability of the multiprocessor system. In this paper, we determine the exact value of λh(FQn) for integer h, 1≤h≤2⌈n2⌉+1 and 6≤n, which generalizes several known results for h≤n. More interestingly, we also show that λh(FQn) is the constant (⌈n2⌉−r+1)2⌊n2⌋+r for 2⌊n2⌋+r−lr≤h≤2⌊n2⌋+r, where r=1,2,…,⌈n2⌉−1 and lr=22r−13 if n is odd and lr=22r+1−23 if n is even. In particular, for r=⌈n2⌉−1, ⌊2n+23⌋≤h≤2n−1, λh(FQn)=2n.