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

The folded hypercube FQ n , as a variation of the hypercube Q n , 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 λ h ( FQ n ) for integer h, 1 ? h ? 2 ? n 2 ? + 1 and 6 ? n , which generalizes several known results for h ? n . More interestingly, we also show that λ h ( FQ n ) is the constant ( ? n 2 ? - r + 1 ) 2 ? n 2 ? + r for 2 ? n 2 ? + r - l r ? h ? 2 ? n 2 ? + r , where r = 1 , 2 , ? , ? n 2 ? - 1 and l r = 2 2 r - 1 3 if n is odd and l r = 2 2 r + 1 - 2 3 if n is even. In particular, for r = ? n 2 ? - 1 , ? 2 n + 2 3 ? ? h ? 2 n - 1 , λ h ( FQ n ) = 2 n .