A Compact Layout for the Three-Dimensional Tree of Meshes
Applied Mathematics Letters
We provide a simple demonstration that the n×n×n tree of meshes graph truncated to llevels can be embedded in a three-dimensional (3D) grid using volume . The maximum wire length in the embedding of the graph is . This embedding simplifies the method developed by Leighton and Rosenberg  for the 3D embeddings of general graphs and allows the framework of Bhatt and Leighton  for 2D graph layout to be extended to 3D. It also leads to good 3D layouts for various fat-tree routing networks [8,2] and the 3D meshes of trees graph .
Applied Mathematics Letters, Volume 1, Issue 2, 1988, Pages 171–176
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Copyright © 1988 Published by Elsevier Ltd.