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 lambda(h),(FQ(n)) for integer h, 1 <= h <= 2(inverted) (right perpendicular) (n/2) (inverted) (left perpendicular+1) and 6 <= n, which generalizes several known results for h <= n. More interestingly, we also show that lambda(h) (FQ(n)) is the constant (inverted right perpendicular n/2 inverted left perpendicular - r + 1)2(left perpendicular n/2 right perpendicular+r) for 2(left perpendicular n/2 right perpendicular+r) - l(r) <= h <= 2(left perpendicular n/2 right perpendicular+r), where where r = 1, 2, ... , inverted right perpendicular n/2 inverted left perpendicular - 1 and l(r) = 2(2r)-1/3 if n is odd and l(r) = 2(2r+1)-2/3 if n is even. In particular, for r = inverted right perpendicular n/2 inverted left perpendicular - 1, left perpendicular 2(n)+2/3right perpendicular <= h <= 2(n-1), lambda(h)(FQ(n)) = 2(n). (c) 2015 Elsevier B.V. All rights reserved.