Embedding binary trees into crossed cubes

The recently introduced interconnection network, crossed cube, has attracted much attention in the parallel processing area due to its many attractive features. Like the ordinary hypercube, the n-dimensional crossed cube is a regular graph with 2ⁿ vertices and n2^n-1 edges. The diameter of the crossed cube is approximately half that of the ordinary hypercube. These advantages of the crossed cube motivated the study of how well it can simulate other networks such as the complete binary tree. We show that the (2ⁿ -1) node complete binary tree can be embedded into the n-dimensional crossed cube with dilation 1