This Article 
 Bibliographic References 
 Add to: 
Embedding Graphs onto the Supercube
April 1995 (vol. 44 no. 4)
pp. 593-597

Abstract—In this paper we consider the Supercube, a new interconnection network derived from the Hypercube. The Supercube, introduced by Sen in [10], has the same diameter and connectivity as a Hypercube but can be realized for any number of nodes, not only powers of 2.

We study the Supercube’s ability to execute parallel programs, using graph-embedding techniques. We show that complete binary trees and bidimensional meshes (with a side length power of 2) are spanning subgraphs of the Supercube. We then prove that the Supercube is Hamiltonian and, when the number of nodes is not a power of 2, it contains all cycles of length greater than 3 as subgraphs.

[1] V. Auletta,A.A. Rescigno,, and V. Scarano,“On the fault tolerance andcomputational capabilities of the Supercube,” Proc. IV Italian Conf.Theoretical Computer Science,L’Aquila, Italy, Oct. 1992.
[2] V. Auletta,A.A. Rescigno,, and V. Scarano,“Fault tolerant routing in theSupercube,” Parallel Processing Letters, vol. 3, no. 4, pp. 393-405, 1993.
[3] L. Bhuyan and D.P. Agrawal,“Generalized Hypercubes and Hyperbus structurefor a computer network,” IEEE Trans. Computers, vol. 33, pp. 323-333, 1984.
[4] S. Bhatt,F. Chung,F.T. Leighton,, and A. Rosenberg,“Optimal simulation of tree machines,” Proc. 27th IEEE Symp. Foundations of Computer Science, pp. 274-282, 1986.
[5] S.L. Johnsson, "Communication Efficient Basic Linear Algebra Computations on Hypercube Architectures," J. Parallel and Distributed Computing, vol. 4, pp. 133-172, 1987.
[6] H.P. Katseff, "Incomplete Hypercubes," IEEE Trans. Computers, vol. 37, no. 5, pp. 604-608, May 1988.
[7] A. Rosenberg,“Cycles in networks,” Technical Report 91-20 of Computer and Information Science Dept.,Univ. of Massachusetts at Amherst, 1991.
[8] A.L. Rosenberg,“Product-shuffle networks: Toward reconciling shuffles and butterflies,” Discrete Applied Mathematics, vol. 37/38, pp. 465-488, July 1992.
[9] Y. Saad and M. Schultz, "Topological Properties of Hypercubes," IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988.
[10] A. Sen,“Supercube: An optimally fault tolerant network architecture,” Acta Informatica, vol. 26, pp. 741-748, 1989.
[11] A. Sen, A. Sengupta, and S. Bandyopadhyay, "On the Routing Problem in Faulty Supercubes," Information Processing Letters, vol. 42, pp. 39-46, Apr. 1992.
[12] M. Yoeli,“Binary ring sequences,” Am. Math. Monthly, vol. 69, pp. 852-855, 1962.
[13] S.-M. Yuan,“Topological properties of supercube,” Information Processing Letters, vol. 37, pp. 241-245, 1991.

Index Terms:
Cycles, graph embedding, Hamiltonian cycle, parallel architectures, Supercube.
Adele Anna Rescigno, Vincenzo Auletta, Vittorio Scarano, "Embedding Graphs onto the Supercube," IEEE Transactions on Computers, vol. 44, no. 4, pp. 593-597, April 1995, doi:10.1109/12.376173
Usage of this product signifies your acceptance of the Terms of Use.