Abstract. The locally twisted cube is a newly introduced interconnection network for parallel computing, which possesses many desirable properties. In this paper, the problem of embedding complete binary trees into locally twisted cubes is studied. Let LT Q n (V, E) denote the n-dimensional locally twisted cube. We find the following result in this paper: for any integer n ≥ 2, we show that a complete binary tree with 2 n − 1 nodes can be embedded into the LT Q n with dilation 2.

The WK-recursive network denoted by K(d, t) has received much attention due to its many favorable properties. We use O i to denote the open vertex set of K i (d, t−1) with 1 ≤ i ≤ d and let O I = {O i |1 ≤ i ≤ d}. We prove that given any node μ and a set of distinct destination nodes T = {t j |1 ≤ j ≤ d−1} where t j ∉ O I , and μ, t j are not in the same subgraph, there exist d−1 node-disjoint paths between μ and T whose union covers all the vertices of K(d, t) where d≥4 and t≥1.

As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, binomial tree embeddings in locally twisted cubes are studied. We present two major results in this paper: (1) For any integern≥ 2, ann-dimensional binomial treeBncan be embedded inLTQnwith dilation 1 by randomly choosing any vertex inLTQnas the root. (2) For any integern≥ 2, ann-dimensional binomial treeBncan be embedded inLTQnwith up ton− 1 faulty links inlog(n− 1) steps where dilation = 1. The results are optimal in the sense that the dilations of all embeddings are 1.