Abstract

The interconnection network considered in this paper is the folded hypercube that is an attractive variance of the well-known hypercube. The folded hypercube is superior to the hypercube in many criteria, such as diameter, connectivity and fault diameter. In this paper, we study the path embedding aspects, bipanconnectivity and m-panconnectivity, of the n-dimensional folded hypercube. A bipartite graph is bipanconnected if each pair of vertices x and y are joined by the bipanconnected paths that include a path of each length s satisfying and is even, where N is the number of vertices, and denotes the shortest distance between x and y. A graph is m-panconnected if each pair of vertices x and y are joined by the paths that include a path of each length ranging from m to N−1. In this paper, we introduce a new graph called the Path-of-Ladders. By presenting algorithms to embed the Path-of-Ladders into the folded hypercube, we show that the n-dimensional folded hypercube is bipanconnected for n is an odd number. We also show that the n-dimensional folded hypercube is strictly (n−1)-panconnected for n is an even number. That is, each pair of vertices are joined by the paths that include a path of each length ranging from n−1 to N−1; and the value n−1 reaches the lower bound of the problem.

Keywords: Interconnection networks; Algorithms; Panconnectivity; Folded hypercubes