Panconnectivity of n-dimensional torus networks with faulty vertices and edges

AbstractThe torus network is one of the most popular interconnection topologies for massively parallel computing systems. In this paper, we mainly consider the p-panconnectivity of n-dimensional torus networks with faulty elements (vertices and/or edges). A graph G is said to be p-panconnected if for each pair of distinct vertices u,v∈V(G), there exists a (u,v)-path of each length ranging from p to |V(G)|−1. A graph G is m-fault p-panconnected if G−F is still p-panconnected for any F⊆V(G)∪E(G) with |F|≤m. By using an introduction argument, we prove that the n-dimensional torus T2k1+1,2k2+1,…,2kn+1 is ∑i=1nki-panconnected and (2n−3)-fault [∑i=1n(ki+1)−1]-panconnected