Volumes of 3D drawings of homogenous product graphs (extended abstract)

Abstract

3-dimensional layout of graphs is a standard model for orthogonal graph drawing. Vertices are mapped into the 3D grid and edges are drawn as the grid edge disjoint paths. The main measure of the efficiency of the drawing is the volume which is motivated by the 3D VLSI design. In this paper we develop a general framework for efficient 3D drawing of product graphs in both 1 active layer and general model. As a consequence we obtain several optimal drawings of product graphs when the factor graphs represent typical networks like CCC, Butterfly, star graph, De Bruijn... This is an analogue of a similar work done by Fernandez and Efe [2] for 2D drawings using a different approach. On the other hand our results are generalizations of the optimal 3D drawings of hypercubes [9]. © Springer-Verlag Berlin Heidelberg 2005.