Embedding graphs onto the Supercube

Abstract

In this paper we consider the Supercube, a new interconnection network derived from the hypercube. The Supercube, introduced by A. Sen (1989), 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>