Reliability analysis of bijective connection networks in terms of the extra edge-connectivity

Reliability evaluation of interconnection network is of significant importance to the design and maintenance of multiprocessor systems. The extra edge-connectivity (also called restricted edge-connectivity) is an important parameter for the reliability evaluation of interconnection network. In this paper, we find a method to study the h-extra edge-connectivity of an n-dimensional bijective connection network (in brief, BC network, also called hypercube-like network). As an application, we determine h-extra edge-connectivity of an n-dimensional BC network is a constant 2n-1 for 2n-1+2f3⩽h≤2n-1,n⩾4, where f=0 when n is even, and f=1 when n is odd. We also show that the lower bound of h is sharp. This paper also obtains the exact value of h-extra edge-connectivity of an n-dimensional BC network for 1⩽h⩽2⌊n2⌋+1,n⩾4. Besides, since the BC network includes several well-known network models, such as, hypercubes, twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes, generalized twisted cubes and Mcubes, so the previous results on the h-extra edge-connectivity of these networks are our corollaries.