Complete binary trees embeddings in Möbius cubes

• We propose an approach to embed the complete binary tree into the n  -dimensional Möbius cube MnMn.
• We prove that the complete binary tree with 2n−12n−1 vertices can be embedded with dilation 1, congestion 1, load 1 into MnMn and expansion tending to 1.
• The research result in this paper demonstrates that embeddability of the complete binary tree in the n-dimensional Möbius cube is superior to that in the n-dimensional hypercube.

The complete binary tree as an important network structure has long been investigated for parallel and distributed computing, which has many nice properties and used to be embedded into other interconnection architectures. The Möbius cube MnMn is an important variant of the hypercube QnQn. It has many better properties than QnQn with the same number of edges and vertices. In this paper, we prove that the complete binary tree with 2n−12n−1 vertices can be embedded with dilation 1, congestion 1, load 1 into MnMn and expansion tending to 1.