On the Topological properties of Generalized Hypercubes

Nestine Hope S. Hernandez

(MS Graduated: Summer 2009)

Abstract

In this thesis, we study the topological properties of the generalized hypercube. We define a generalized hypercube denoted by Q(d1, d2,…,dn) as a graph whose vertex set is the set V = {0, 1,…,di – 1}, 1 ≤ i ≤ n} such that two vertices are adjacent whenever they differ in exactly one coordinate. In this study we will obtain exact values for the bisection width, cut width and total edge length of the generalize hypercube. We will show isomorphisms between Q(d1, d2,…,dn) and Q(da1, da2,…,d an) where a1a2 … an is any permutation of 12 … n. We will also show some excellent features of generalized hypercube graphs such as the embedding of other network topologies.