MATRIX REPRESENTATION OF GRAPH EMBEDDING IN A HYPERCUBE

The purpose of this paper is to demonstrate the use of matrices for the representation of graph embedding in a hypercube. We denote the image of an embedding (which is a subgraph of the hypercube) as a matrix. With this representation, we are able to simplify, unify, generalize, or improve existing results regarding multigraph embedding in a hypercube. A class of trees called regular binary-reflected trees is identified, which includes linear paths, binomial trees, and many others. We show that for any regular binary-reflected tree T, n copies of T can be simultaneously embedded in an n-cube with congestion = 2. Embeddings of binary trees and meshes are also discussed. (C) 1994 Academic Press, Inc.