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

Abstract

The n-dimensional torus T(k1,k2,…,kn) (including the k-ary n-cube Qnk) 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 ki≥3 for i=1,2,…,n, with at most one ki being even, then T(k1,k2,…,kn) 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].