Complete binary trees embeddings in Möbius cubes

Abstract

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 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 2n−1 vertices can be embedded with dilation 1, congestion 1, load 1 into Mn and expansion tending to 1.