Embedding Complete Binary Trees CBTn into Augmented Cubes AQn

As an important network structure, the complete binary tree has been investigated for parallel and distributed computing as well as being embed into other interconnection architectures for its nice properties. The n-dimensional augmented cube AQ
n
is an important variant of the hypercube Q
n
. It has many attractive features superior to those of the hypercube. In this paper, we prove that the complete binary tree CBT
n
with 2
ⁿ
vertices can be embedded into AQ
n
with dilation 1 and congestion 1.