The bipanconnectivity and m -panconnectivity of the folded hypercube

• Published in: Theoretical computer science Vol. 385; no. 1; pp. 286 - 300
• Main Author: Fang, Jywe-Fei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.10.2007; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Computer science; control theory; systems; Exact sciences and technology; Folded hypercubes; Information retrieval. Graph; Interconnection networks; Miscellaneous; Panconnectivity; Theoretical computing; Folded hypercubes; Algorithms; Interconnection networks; Panconnectivity; Interconnection network; Lower bound; Graph path; Computer theory; Embedding; Algorithm; Variance; Graph connectivity; Interconnection; Hypercube; Bipartite graph; Distance
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2007.07.005

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 N − 1 ≥ s ≥ dist ( x , y ) and s - dist ( x , y ) is even, where N is the number of vertices, and dist ( x , y ) 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.