Complete binary trees embeddings in Möbius cubes

We propose an approach to embed the complete binary tree into the n-dimensional Mbius cube Mn.We prove that the complete binary tree with 2n1 vertices can be embedded with dilation 1, congestion 1, load 1 into Mn and expansion tending to 1.The research result in this paper demonstrates that embeddability of the complete binary tree in the n-dimensional Mbius 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 Mbius cube Mn is an important variant of the hypercube Qn. It has many better properties than Qn with the same number of edges and vertices. In this paper, we prove that the complete binary tree with 2n1 vertices can be embedded with dilation 1, congestion 1, load 1 into Mn and expansion tending to 1.