Edge-fault tolerance of hypercube-like networks

Abstract

This paper considers a kind of generalized measure λs(h) of fault tolerance in a hypercube-like graph Gn which contains several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes, crossed cubes, Möbius cubes and the recursive circulant G(2n,4), and proves λs(h)(Gn)=2h(n−h) for any h with 0≤h≤n−1 by the induction on n and a new technique. This result shows that at least 2h(n−h) edges of Gn have to be removed to get a disconnected graph that contains no vertices of degree less than h. Compared with previous results, this result enhances fault-tolerant ability of the above-mentioned networks theoretically.