Embedding meshes into crossed cubes

Jianxi Fan, Xiaohua Jia

Abstract: Crossed cubes are important variants of hypercubes. In this paper, we consider embeddings of meshes in crossed cubes. The major research findings in this paper are: (1) For any integer n ⩾ 1, a 2 × 2n−1 mesh can be embedded in the n-dimensional crossed cube with dilation 1 and expansion 1. (2) For any integer n ⩾ 4, two node-disjoint 4 × 2n−3 meshes can be embedded in the n-dimensional crossed cube with dilation 1 and expansion 2. The obtained results are optimal in the sense that the dilations of the embeddings are 1. The embedding of the 2 × 2n−1 mesh is also optimal in terms of expansion because it has the smallest expansion 1.