Three dimensional circuit layouts
SIAM Journal on Computing
On forwarding indices of networks
Discrete Applied Mathematics
Efficient VLSI Layouts for Homogeneous Product Networks
IEEE Transactions on Computers
Edge-forwarding index of star graphs and other Cayley graphs
Discrete Applied Mathematics
Bisection width of transposition graphs
Discrete Applied Mathematics
VLSI layouts of complete graphs and star graphs
Information Processing Letters
Layout volumes of the hypercube
GD'04 Proceedings of the 12th international conference on Graph Drawing
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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].