Paired 2-disjoint path covers of multi-dimensional torus networks with 2n-3 faulty edges

The n-dimensional torus T(k(1),k(2),...,k(n)) (including the k-ary n-cube Q(n)(k)) is one of the most popular interconnection networks. A paired k-disjoint path cover (paired k-DPC for short) of a graph is a set of k disjoint paths joining k distinct source-sink pairs that cover all vertices of the graph. In this paper, we consider the paired 2-DPC problem of n-dimensional torus. Assuming k(i) >= 3 for i = 1,2,..., n, with at most one ki being even, then T(k(1), k(2),..., k(n)) with at most 2n - 3 faulty edges always has a paired 2-DPC. And the upper bound 2n - 3 of edge faults tolerated is optimal. The result is a supplement of the results of Chen [3] and [4]. (C) 2017 Elsevier B.V. All rights reserved.