Embedding graphs onto the Supercube

Abstract

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

Panconnectivity, fault‐tolerant hamiltonicity and hamiltonian‐connectivity in alternating group graphs

“…The existence of pancyclicity in a network is even more useful because it implies that the network can embed cycles with arbitrary length, and therefore, it has been extensively studied. Previous results showed that many interconnection networks are pancyclic, including de Bruijn networks [19,33], Xtrees [23], product-shuffle networks [24], alternating group graphs [18], and supercubes where the number of vertices is not a power of two [2]. Also, two-dimensional meshes [1], two-dimensional toroidal meshes [7], and hypercubes [12] have been shown to be even-pancyclic.…”

Embedding of Cycles in Twisted Cubes with Edge-Pancyclic

“…as guest graphs [5,9,11,13,15,18,20], because these interconnection networks are widely used in parallel computing systems.…”

Complete path embeddings in crossed cubes

“…as guest graphs [1][2][3][4]11,13,14,16,17], because these interconnection networks are widely used in parallel computing systems. Embeddings of paths, cycles, and trees into crossed cubes were studied in [3,6,10,11,14,16].…”